$$NiCl_2(aq) + 2AgNO_3(aq) \rightarrow Ni(NO_3)_2(aq) + 2AgCl(s)$$

Ionic equation

$$Ni^{2+}(aq) + 2Cl^-(aq) + 2Ag^+(aq) + 2NO_3^-(aq) \rightarrow Ni^{2+}(aq) + 2NO_3^-(aq) + 2AgCl(s)$$

Net ionic equation

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