Answer
Balanced equation:
$2NI_3(s) --\gt N_2(g) + 3I_2(g)$
Reaction type: Decomposition.
Work Step by Step
1. Count the atoms of each element in both sides of the reaction.
$NI_3(s) --\gt N_2(g) + I_2(g)$
Reactants: $N = 1$ and $I = 3$
Products: $N = 2$ and $I = 2$
2. Balance the number of nitrogen atoms, by putting a "2" in front of $NI_3$.
$2NI_3(s) --\gt N_2(g) + I_2(g)$
3. Balance the number of iodine atoms, by putting a "3" in front of $I_2$
$2NI_3(s) --\gt N_2(g) + 3I_2(g)$
4. Classify the reaction.
That reaction follows the pattern of a decomposition reaction (AB $--\gt$ A + B). Where one single compound splits into two products.