I feel like you're trolling me, but I'll assume that you're not. Among your several posts in this thread, you have provided multiple versions of your data. In the moment, all we have to work with is what you provide us. When you later provide us something different, it's confusing. You seem to expect that we'll just intuit what you really want, and so you seem unwilling to provide explicit (i.e. with actual code instead of text) specifications of what you want. I will try (again) to be as clear as I can about what you've said (I'm copying and pasting exactly from your posts):

At one point you gave us this (which I've named earlierVersionOfData)

earlierVersionOfData = {{{2, 3}}, {{4, 5}, {6, 7}, {9, 8}}, {{{8, 4}, {6, 9}}, {{3, 5}, {5, 2}, {7, 8}}}}

We can use TreeForm to more easily see the structure:

TreeForm[earlierVersionOfData]

It's clearly not totally balanced. In a later post, you provided this (I'm naming the outer list latestVersionOfData and I'm using the set1 convention you used for each day):

set1 = {{2, 7}};
set2 = {{3, 4}, {5, 6}};
set3 = {{7, 8}, {9, 10}, {10, 11}};
set4 = {{2, 3}, {3, 4}};
latestVersionOfData = {{set1}, {set2}, {set3}, {set4}}

Again, let's use TreeForm

TreeForm[latestVersionOfData]

This data is now balanced, but is deeper than it needs to be (and deeper than how your words describe it). Now, here's what I'm assuming you actually have as your data:

ericsVersionOfData = {{{2, 7}}, {{3, 4}, {5, 6}}, {{7, 8}, {9, 10}, {10, 11}}, {{2, 3}, {3, 4}}};
TreeForm[ericsVersionOfData]

Do you now see the difference? And do you maybe now appreciate how actual code is less ambiguous than your text-only descriptions? But regardless, I don't really care, because this is your project and not mine. Have I given you something helpful, or are you still at a loss? Shall we continue this side discussion about why your posts are confusing, or should we move on to actually solving your problem? Up to you.

Well, that sounds much clearer, but it doesn't match what you said previously. Specifically, this

 {{set1}, {set2}, {set3}, {set4}, {set5} ..., {set15}}

is not the same structure as this

{{{2, 3}}, {{4, 5}, {6, 7}, {9, 8}}, {{{8, 4}, {6, 9}}, {{3, 5}, {5, 2}, {7, 8}}}}

Since you indicated that you're struggling with Mathematica syntax, let me digress a moment and make this as explicit as I can. In this expression,

{{{2, 3}}, {{4, 5}, {6, 7}, {9, 8}}, {{{8, 4}, {6, 9}}, {{3, 5}, {5, 2}, {7, 8}}}}

we have a list of 3 elements. That would presumably represent 3 days worth of readings. Day 1 had a reading from a single instrument. Day 2 had readings from 3 instruments. But day 3 doesn't fit the pattern. It looks like that third element is actually two more days worth of data: a day with 2 readings and a day with 3 readings. Do you understand my confusion now?

Your new description,

 {{set1}, {set2}, {set3}, {set4}, {set5} ..., {set15}}

is consistent with what you've described, but there is still some confusion for me, because you've inserted an extra layer of brackets. You've said that set1 is {{2,7}}, and set2 is {{3,4}, {5,6}} and so forth. So, the expression

 {{set1}, {set2}, {set3}, {set4}, {set5} ..., {set15}}

becomes, when fully expanded out,

 {{{{2,7}}}, {{{3,4}, {5,6}}}, {{{7,8}, {9,10}, {10,11}}}, {{{2,3}, {3,4}}}, ... }

Now, maybe that's what your data actually looks like, but it doesn't seem like it should based on your verbal description.

So, because of all of that, I'm going to assume that your data actually looks like this (just 4 days, and I'm going to assign it to a variable so we can easily operate on it):

data = {{{2, 7}}, {{3, 4}, {5, 6}}, {{7, 8}, {9, 10}, {10, 11}}, {{2, 3}, {3, 4}}}

Now, at this point, you could map BarChart over this data, wrap it in a Row and we have something that might be what you want:

Row[BarChart /@ data]

But I'm still confused, because you said that the pairs at the lowest level represent a code and a frequency. Since you have two different semantics within each pair, it doesn't seem like you just want to apply BarChart to it. It sounds like you would want to chart the frequencies and use the code as a label. So, an alternate interpretation might be something like this (I'm switching to Grid because I like its options better):

Grid[{BarChart /@ Map[Apply[Labeled]@*Reverse, data, {-2}]}, Alignment -> {Center, Bottom}]

I hope that helps. Maybe it's not what you want, but maybe it'll help you find your way. If I'm still off the mark, then all I can say is what I've already said: give us a picture or actual data or actual code that gets rid of all the ambiguity inherent in your verbal descriptions.

A picture of what? which code? I have nothing of the sort.

You said in your original post:

it only works when I set a loop, like For i to n, barchart each element (i) of the list

That led me to believe that you were able to achieve an approximation of what you want using a for loop. If you just provide us with that code, we can run it ourselves and see what you're trying to achieve. As for a picture, the picture would either be the result of the for loop, or just something you drew yourself to represent what you want. If you know what you want the result to look like for a given input, then you can draw a picture of that or write "fake" code that creates a picture in a hard-coded fashion. Whatever. Just something that reduces the ambiguity.

I hate to belabor this, but you keep saying surprising things. Here is an exact quote of what you just recently said:

{{{2, 3}}, {{4, 5}, {6, 7}, {9, 8}}, {{{8, 4}, {6, 9}}, {{3, 5}, {5, 2}, {7, 8}}}}, this is it! my data is structured in exactly the same way, please consider all single pairs as a nested list as well as i just did to the first one {{2,3}}. My list nl just carries on along the same structure, namely, single pair, 2 pairs, 3 pairs...for over 100 lists. I can't be clearer than this.

Well, maybe you can't be clearer, but this is absolutely, definitely, NOT clear. A list that is "shaped" like "single pair, 2 pairs, 3 pairs, etc" would look like this:

{{{1,2}}, {{3,4}, {5,6}}, {{7,8}, {9,10}, {10,11}}}

but your nl has deeper structure than this. In words, your nl is "single pair, three pairs, a list with two sublists that themselves contain 2 pairs and 3 pairs". I see no obvious pattern here, so I have no idea what to expect next. I have no idea how deep this structure will go.

But now we're just arguing over how clear your language has been to this point. And that really doesn't matter. We're trying to give you suggestions for how to improve your question, but you just keep insisting that you've already been perfectly clear. Well, that's fine. Just don't expect us to be very helpful, because we're stumped until you give us more to go on. It's your project. Up to you whether the effort is worth it.

Hello Michael, Thanks for your reply. I am afraid i don't understand at all where you are coming from when you say i quote " it would really be much easier if you showed us a picture or gave us the code that almost works so we don't have to keep guessing at how to interpret your words"

A picture of what? which code? I have nothing of the sort.

I have only my data which i managed to set into nested lists as i have explained, and the sample you chose is good one, notably, {{{2, 3}}, {{4, 5}, {6, 7}, {9, 8}}, {{{8, 4}, {6, 9}}, {{3, 5}, {5, 2}, {7, 8}}}}, this is it! my data is structured in exactly the same way, please consider all single pairs as a nested list as well as i just did to the first one {{2,3}}. My list nl just carries on along the same structure, namely, single pair, 2 pairs, 3 pairs...for over 100 lists. I can't be clearer than this. I have nothing else no picture no code. As i admitted i am a beginner with Mathematica and i was happy having so far been able to set my data into a nested list like i did. Again, all i want is to be able to plot about 15 (+/-5 depending on the requirement but this should not be relevant to you) of my nested lists as separate sets of bar charts (each nested set showing 2 bars of different colors for each pair (which represent a code and a frequency if you must know) it contains either 1 pair,2 pairs, or 3 pairs)) next to each other in a row. From your feedback, i am guessing you are complicating the issue by thinking too much.

Moreover, i am altogether surprised when you say "You can berate us or you can give us what we're asking for so that you can get your problem solved" How can i berate you when i am trying to learn from you. And how can i be holding something to stop you from helping me? You are wrong here,

Anyway, i thank you again and trust with the above clarification, you would catch my drift .

Sincerely, Adam Cherad

Hi MiChael,
I just looked closer at the bar charts you produced but you seem to have considered only the 2nd number of the pair. I apologize for the confusion; it is clear i am a beginner learning Mathematica, and obviously, my vision is still warped with articulating the critical pivots for an experienced programmer. Anyway, in case you are still interested at wasting few more moments of your time, i clarify as follows:
You took the sample
nl = {{2, 3}, {{4, 5}, {6, 7}, {9, 8}}, {{{8, 4}, {6, 9}}, {{3, 5}, {5, 2}, {7, 8}}}}; and for this sample what i expected were (ignoring the first list {2,3} which i will nest later),
1) One bar chart set for {{4, 5}, {6, 7}, {9, 8}} with 3 pairs of bars (4-5), (6-7), and (9-8) (call it set1 as a legend), meaning each one of the numbers in the pair should be reflected by a bar.
2) and next to it another Bar chart for {{8, 4}, {6, 9}}, with 2 pairs of bars (8-4) and (6-9) (call it set2) and
3) then another for {{3, 5}, {5, 2}, {7, 8}} with 3 pairs of bars (3-5), (5-2), (7-8) call i t set 3) I hope it is clearer
Adam Cherad

Nope, still don't get it. I need an example nl. I, too, am truly taken aback by how difficult it is to provide a small working example. The bar charts you show in a row lack legends, even though I explicitly asked about them.

Here's another shot in the dark, probably still wrong:

nl = {{2, 3}, {{4, 5}, {6, 7}, {9, 8}}, {{{8, 4}, {6, 9}}, {{3, 5}, {5, 2}, {7, 8}}}};
GraphicsRow@
 Cases[nl, 
  data_?MatrixQ :> 
   BarChart[data[[All, 2]], ChartLegends -> data[[All, 1]]], Infinity]

Please note that {2, 3} is left off. There is "a separate legend for each nest of either 1 pair, 2 pairs or 3 pairs," but {2, 3} is not in a "nest."

I guess I should just stop. It's an obvious thing, and I don't see it. I'm probably not helping. Good luck! Someone else will probably show me where I'm confused.

By opening my post with "my interpretation," I meant to imply I wasn't confident I understood what was desired. I'm still not. My suggestion at the end of my post is "to give a simple example of nl...and show exactly what you want the arguments of BarChart to become." Maybe drawing what you want would be easier, if you don't know how to do it with BarChart.

Have you seen GraphicsRow[]? It's a way to arrange several bar charts in a row. And some people just use Row[], which is a way to arrange any expressions in a row.

In your example in the OP, {a,b} is a pair at level 1; {c, d} is on level 2, apparently (again, I'm interpreting) to be grouped with the following two pairs; at the end we get {h, j} at level 1 but not, I suppose, to be group with {a, b}, even though both are at the same level. I don't know if there are pairs at deeper levels. You mention hundreds of nested lists, and the lack of a consistent structure leads me to imagine arbitrary levels of nesting. Further I cannot imagine putting hundreds of bar charts in a row and have it be legible. I'm just confused.

Without an example, I do not think I can help further.

Hello Eric
"Does that mean you just want multiple BarCharts but arranged more elegantly?" Yes, but it is not for elegance, i need to see the multiple Barchart in one row for other purposes,
Thanking you.

Hello Michael,
Many thanks for your time.
The problem with Level 2, is that it opens up all the nested lists into individual pairs, that defeats the issue because Iike the nested pairs to be shown in the barchart as a group.
Put simply, I have nested lists of
1 pair of elements {{a,b}},
2 pairs {{a,e},{b,a}} and
3 pairs {{a,c}, {b,d}, {e,a}}
All elements are integer numbers (All the pairs are made up of a code (integer) and a counter, or a frequency (also an integer).
I like the barchart to show them next to each other in a row, but with a separate legend for each nest of either 1 pair, 2 pairs or 3 pairs.
Thank you again