Answer
20 diagonals.
Work Step by Step
We must select two vertices among eight vertices. The order in which they are selected is not important. So, we have $_8C_2$ different combinations:
$_8C_2=\frac{8!}{(8-2)!~2!}=\frac{8\times7\times6!}{6!~2!}=28$
But, among those 28 combinations, 8 are sides.
$Diagonals=28-8=20$
