The balanced equation for the reaction of lithium hydride (LiH) with aluminum chloride (AlCl₃) is:

3 LiH + AlCl₃ → AlH₃ + 3 LiCl

Explanation:

* Reactants: Lithium hydride (LiH) and aluminum chloride (AlCl₃)

* Products: Aluminum hydride (AlH₃) and lithium chloride (LiCl)

This reaction is a double displacement reaction, where the lithium and aluminum ions exchange their anions.

Note: Aluminum hydride (AlH₃) is a highly reactive and unstable compound, and this reaction is difficult to control. It's typically used in specialized applications like reducing agents in organic chemistry.