Answer
$$2HNO_3(aq) + Na_2SO_3(aq) \longrightarrow SO_2(g) + H_2O(l) + 2NaNO_3(aq)$$
Work Step by Step
1. This reaction has a sulfite and an acid as its reactants. Thus, it will produce $SO_2(g)$, $H_2O(l)$ and a salt made of the other ions:
$$HNO_3(aq) + Na_2SO_3(aq) \longrightarrow SO_2(g) + H_2O(l) + Salt$$
The remaining ions are: $Na^{+}$ and $N{O_3}^-$, therefore, the salt is $NaNO_3$:
$$HNO_3(aq) + Na_2SO_3(aq) \longrightarrow SO_2(g) + H_2O(l) + NaNO_3(aq)$$
2. Now, balance the equation.
To balance the number of sodium atoms, put a $2$ before $NaNO_3$
$$HNO_3(aq) + Na_2SO_3(aq) \longrightarrow SO_2(g) + H_2O(l) + 2NaNO_3(aq)$$
To balance the number of Nitrogen atoms, to the same for $HNO_3$:
$$2HNO_3(aq) + Na_2SO_3(aq) \longrightarrow SO_2(g) + H_2O(l) + 2NaNO_3(aq)$$
