Balance: MgCl2(aq) + AgNO3(aq) -> AgCl(s) + Mg(NO3)2(aq)

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Balance: MgCl2(aq) + AgNO3(aq) -> AgCl(s) + Mg(NO3)2(aq)

nitrate, NO_3 comes from the AgNO_3.

chloride, Cl comes from the MgCl_2.

You need 2 chlorides (chlorine atoms) and two nitrate ions. That should be enough to figure out how to balance it.