Drawing a diagonal means to connect a vertex with another non-adjacent vertex.
So, for each vertex, we have 8-3=5 possible diagonals. This leads to a total of 8*5=40 diagonals.
We have to divide this number by 2 though, because in this way we're counting each diagonal twice (connecting points AB or BA gives the same diagonal).
So, an 8 sided shape has 20 diagonals.