Answer
There are 2 hydroxide ions.
Work Step by Step
In $Ca_{2}Mg_{5}Si_{8}O_{22}(OH)_{x}$, $Ca^{2+}$ contributes total +4 charge, $Mg^{2+}$ contributes total +10 charge, $Si_{8}O_{22}$ contributes total -12 charge. So, to balance charges, $OH^{-}$ contributes total -2 charge. Thus, there are 2 $OH^{-}$ ions.
