The balanced equation for aqueous ammonium chloride and lead II nitrate is:

$$Pb(NO_3)_2(aq) + 2NH_4Cl(aq) → PbCl_2(s) + 2NH_4NO_3(aq)$$

In this reaction, lead II nitrate and ammonium chloride react to form lead II chloride and ammonium nitrate. The products are insoluble lead II chloride and soluble ammonium nitrate.