Here's the balanced chemical equation for the reaction:
Al₂(SO₄)₃ (aq) + 6 NH₄OH (aq) → 2 Al(OH)₃ (s) + 3 (NH₄)₂SO₄ (aq)
This reaction is a double displacement reaction, where the cations and anions of the reactants switch places. Aluminum hydroxide is a white, gelatinous precipitate that forms in the reaction.