Hi Livia
It would help if you posted the code you tried and explain what you mean by "Mathematica won't seem to allow a vertical shift". Is this what you are looking for?
Plot[8.21 Sin[x] + 20.3, {x, 0, 2 Pi},
AxesOrigin -> {0, 0},
PlotTheme -> "Detailed"]
Remove AxesOrigin -> {0, 0}
and compare. WL has adjusted the origin so the plot is more "centered", but it is still offset.