The balanced molecular equation for the reaction between magnesium chloride and silver nitrate is:

$$\text{MgCl}_2(aq) + 2\text{AgNO}_3(aq) \rightarrow \text{Mg(NO}_3)_2(aq) + 2\text{AgCl}(s)$$

The complete ionic equation is:

$$\text{Mg}^{2+}(aq) + 2\text{Cl}^-(aq) + 2\text{Ag}^+(aq) + 2\text{NO}_3^-(aq) \rightarrow \text{Mg}^{2+}(aq) + 2\text{NO}_3^-(aq) + 2\text{AgCl}(s)$$

The net ionic equation is:

$$\text{2Ag}^+(aq) + 2\text{Cl}^-(aq) \rightarrow 2\text{AgCl}(s)$$