Balancing ionic equations and determining number of ions
Actually $Mg(OH)_2$ has (low) solubility ($K_{sp}=1.5\cdot 10^{-11}$). Since it is asking for the net ionic equation, the only ions reacting (since $NO_3^-$ stays in solution) are $H^+$ and $OH^-$.

You forgot that each molecule of ammonium carbonate produces 3 ions, so multiply your answer by 3.