The balanced equation for the reaction between barium chloride and ammonium carbonate is:

BaCl2 (aq) + (NH4)2CO3 (aq) → BaCO3 (s) + 2NH4Cl (aq)

In this reaction, barium chloride and ammonium carbonate react in aqueous solution to form barium carbonate and ammonium chloride. Barium carbonate is a white solid, while ammonium chloride is a white crystalline solid.