You have the ##K_(sp)## expression, which was explained in the other thread http://socratic.org/questions/in-which-of-the-following-aqueous-solutions-would-you-expect-to-agbr-to-have-the168330.
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.
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