Answer
9 diagonals.
Work Step by Step
We must select two vertices among six vertices. The order in which they are selected is not important. So, we have $_6C_2$ different combinations:
$_6C_2=\frac{6!}{(6-2)!~2!}=\frac{6\times5\times4!}{4!~2!}=15$
But, among those 15 combinations, six are sides.
$Diagonals=15-6=9$
