Answer
Balanced equation: $Si_3N_4(s) --\gt 3Si(s) + 2N_2(g)$
Reaction type: Decomposition.
Work Step by Step
$Si_3N_4(s) --\gt Si(s) + N_2(g)$
1. Balance the number of nitrogen atoms, by putting a "2" in front of $N_2$.
$Si_3N_4(s) --\gt Si(s) + 2N_2(g)$
2. Balance the number of silicon atoms, by putting a "3" in front of $Si$
$Si_3N_4(s) --\gt 3Si(s) + 2N_2(g)$
3. Classify the reaction.
That reaction follows the pattern for a decomposition reaction (AB −−> A + B).