First, you must complete and balance the overall reaction.
Then you must decide which (if any) ions are changing oxidation state (no, in this case) or physical solubility. Ammonium acetate is fairly soluble in water (1480g/L). Zinc nitrate is equally soluble (1843 g/L – 3270 g/L, depending on hydrate form).
Therefore, ALL ions will remain in solution as ions, and there is effectively NO “net ionic” reaction, OR you could say that the net ionic reaction is the same as the ionic reaction.