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So you have 3 Cl on the left and 2cl on the right. First off you put a 2 in front of the AlCl3 to give you 6 Cl, and you put a 3 in front of the MgCl2 to also give you 6Cl on the right side. You then have to balance the Mg and Al, so put a 3 in front of the Mg on the left to give you 3Mg, and 2 in front of the Al on the right to give you 2Al.

Your final, balanced formula is 3Mg + 2AlCl3 => 3MgCl2 + 2Al

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