What is the molar solubility of AI (OH) _ 3 in 0.2 MNaOH solution?...

Concept of common $- ion$ will be applicable for $O{H}^{-}$ group.

$\text{Al}{\left(\text{OH}\right)}_{3} ⇌ \mathop{\text{A}{\text{l}}^{\text{3+}}}_{\text{S}} + \mathop{3\left(\text{O}{\text{H}}^{-}\right)}_{\left(3s + 0.2\right)}$

$Ksp$ for $Al{\left(OH\right)}_{3} = 2.4 \times {10}^{- 24} = s{\left(3s + 0.2\right)}^{3}$

Looking at $Ksp,$ it is clear that $s$ will be much lesser than $0.2 .$

Or, $s ≪ 0.2$

$s \times {\left(0.2\right)}^{3} = 2.4 \times {10}^{- 24} ⇒ s = 2.4 \times {10}^{- 24} / 0.008$
or, $s = 3 \times {10}^{- 22}$