Answer
There are 4 hydroxide ions.
Work Step by Step
In $Al_{2}Si_{2}O_{5}(OH)_{x}$, $Al^{3+}$ contributes total +6 charge, $Si_{2}O_{5}$ contributes total -2 charge. So, to balance charges, $OH^{-}$ contributes total -4 charge. Thus, there are 4 $OH^{-}$ ions.
