calculate the volume of 0.50 M NaOH needed to saturate 100.0 ml of 0.50 M Zn(NO3)2 with Zn(OH)2

You don't have enough information because I don't want to calculate anything that may use different Ksp than you have in your text/notes.

Look up the Ksp fo Zn(OH)2
(Zn^2+) = Ksp/(OH^-)^2 and solve for Zn^2+ in mols/L, then M x L (100 mL or 0.1L) = mols.

Then Zn^2+ + 2OH^- ==> Zn(OH)2
Convert mols Zn^2+from above to mols NaOH and convert that to mL using M NaOH.