Here we know the [OH^-] value (how; what is the pH?). Therefore you have the tools to solve for [Zn^(2+)], whose concentration represents the solubility of zinc hydroxide. Remember that hydroxide ion concentration is squared in the K_(sp) expression.
As an extension, it may be speculated that we could reduce the [Zn^(2+)] value to any degree, simply by increasing [OH^-]. Note that at very high levels of [OH^-], we are likely to form complex ions such as, Zn(OH)_4^(2-) (I assure you this species is real). This is a competing equilibrium that can occur.
And so, we address the equilibrium reaction...
Zn(OH)_2(s) rightleftharpoons Zn^(2+) +2HO^-...
For which K_"sp"=[Zn^(2+)][HO^-]^2...
And if we set S="solubility of zinc hydroxide"...IN PURE WATER...
Then...K_"sp"=Sxx(2S)^2=4S^3=3xx10^-16
And so finally, S=""^(3)sqrt((3xx10^-16)/4)=4.22xx10^-6*mol*L^-1...
And so under the given conditions, we can find the mass of zinc hydroxide in solution... 99.42*g*mol^-1xx4.22xx10^-6*mol*L^-1=0.42*mg*L^-1, i.e. less than "1 ppm"...
But in the given problem, [HO^-]=10^(-5)*mol*L^-1...(why?..because pH=9, and K_w=10^-14)...and so...
K_"sp"=Sxx(2S+2xx10^-5)^2 And so S~=K_"sp"/(2xx10^-5)^2=7.5xx10^-7*mol*l^-1...and so the solubility of the salt is reduced tenfold...
