Solid Zn(OH)2 can dissolve in excess strong alkali, because Zn(OH)2 is amphoteric which can neutralize both strong acids and both strong alkalis to form soluble salt.
Zn(OH)2(s) + 2NaOH(aq) → Na2[Zn(OH)4](aq)
or: Zn(OH)2(s) + 2OH^-(aq) → [Zn(OH)4]^2-(aq)
Solid Zn(OH)2 can dissolve in excess NH3 solution, because they react to form a soluble complex.
Zn(OH)2(s) + 4NH3(aq) → [Zn(NH3)4](OH)2(aq)
or: Zn(OH)2(s) + 4NH3(aq) → [Zn(NH3)4]^2+(aq) + 2OH^-(aq)