I renamed the a and b on the left side to avoid recursion and used rules to perform the transformations. Look up Rule, and Replace for more insight.
Kind regards, David
In[1]:= aa = {{{a, b}, {c, d}, {e, f}}, {{1, 2}, {3, 4}, {5, 6}}};
In[2]:= t = {x, z};
In[3]:= bb = {
aa[[1]] /. {e1_, e2_} -> {e1, e2, t[[1]]},
aa[[2]] /. {e1_, e2_} -> {e1, e2, t[[2]]}
}
Out[3]= {{{a, b, x}, {c, d, x}, {e, f, x}}, {{1, 2, z}, {3, 4, z}, {5, 6, z}}}