What is the net ionic equation for the reaction that occurs when aqueous solutions of koh and zncl2 are mixed?

Net ionic equation:

Zn²⁺(aq)  +   2OH⁻(aq)     →    Zn(OH)₂(s)

Explanation:

Chemical equation:

ZnCl₂ + KOH    →   KCl  + Zn(OH)₂

Balanced chemical equation:

ZnCl₂ + 2KOH    →   2KCl  +Zn(OH)₂

Ionic equation;

Zn²⁺(aq)  + 2Cl⁻(aq)  + 2K⁺(aq)  +  2OH⁻(aq)     →   2K⁺(aq)  + 2Cl⁻(aq)   +Zn(OH)₂(s)

Net ionic equation:

Zn²⁺(aq)  +   2OH⁻(aq)     →    Zn(OH)₂(s)

The K⁺  and Cl⁻  are spectator ions that's why these are not written in net ionic equation. The  Zn(OH)₂ can not be splitted into ions because it is present in solid form.

Spectator ions:

These ions are same in both side of chemical reaction. These ions are cancel out. Their presence can not effect the equilibrium of reaction that's why these ions are omitted in net ionic equation.  

i believe you are right for all except the 3rd ( look at sqdancefan his answer is much better)