How do I balance this reaction?

Question

Li3N + Al2(CO3)3--------------->Li2CO3 + AlN

Answer 1

2Li3N + Al2(CO3)3 => 3Li2CO3 + 2AlN

Answer 2

You have to make sure that you have enough of each element/group on the reactant side to provide the product, and that you have integer coefficients.
For example, each aluminium carbonate provides 2 aluminums and 3 carbonate. So there must be 2 aluminiums on the right side. If this happens, you have to have 2 nitrogens on the left side. This requires you to have 6 Li, and on it goes.

So try 2 Li3N + Al2(CO3)3 -> 3 Li2(CO3) + 2 AlN

Answer 3

Do you mean Li3N + Al2(CO3)3 --------------->Li2CO3 + AlN?
Well the balanced equation for that one is:
2Li3N + Al2(CO3)3 --------------->3Li2CO3 + 2AlN
Both the reactants and products have 6Li, 2Al, 2N, 3C, and 9O, hope this helps. =)