Answer
$2AlCl_3(s)+Ca_3N_2(s)\rightarrow 2AlN(s)+3CaCl_2(s)$
Work Step by Step
$AlCl_3(s)+Ca_3N_2(s)\rightarrow AlN(s)+CaCl_2(s)$
Add a coefficient of 2 to $AlN$ to balance the $N$ atoms.
$AlCl_3(s)+Ca_3N_2(s)\rightarrow 2AlN(s)+CaCl_2(s)$
Add a coefficient of 2 to $AlCl_3$ to balance the $Al$ atoms.
$2AlCl_3(s)+Ca_3N_2(s)\rightarrow 2AlN(s)+CaCl_2(s)$
Add a coefficient of 3 to $CaCl_2$ to balance the $Ca$ and $Cl$ atoms.
$2AlCl_3(s)+Ca_3N_2(s)\rightarrow 2AlN(s)+3CaCl_2(s)$
