Answer
$$NH_4I(aq) + NaOH(aq) \longrightarrow NH_3(g) + H_2O(l) + NaI(aq)$$
Work Step by Step
1. This reaction has an ammonium ion and a base in its reactants. Thus, it will produce $NH_3(g)$, $H_2O(l)$ and a salt made of the other ions:
$$NH_4I(aq) + NaOH(aq) \longrightarrow NH_3(g) + H_2O(l) + Salt$$
The remaining ions are: $Na^{+}$ and $I^-$, therefore, the salt is: $NaI(aq)$
$$NH_4I(aq) + NaOH(aq) \longrightarrow NH_3(g) + H_2O(l) + NaI(aq)$$
2. Now, balance the equation.
The equation is already balanced.
