Number of Fe atoms on the reactant side: 1
Number of Fe atoms on the product side: 2
So we will multiply 2 on the left side to FeCl3. Hence it will become;
2FeCl3(aq) + MgO(s) 🡪 Fe2O3(s) + MgCl2 (aq)
Number of Cl atoms on the reactant side: 6 (2 X 3)
Number of Cl atoms on the product side: 2
So we will multiply 3 on the right side to MgCl2. Hence it will become;
2FeCl3(aq) + MgO(s) 🡪 Fe2O3(s) + 3MgCl2 (aq)
Now, the number of Mg atoms are not balanced. In order to balance it, we will multiply 3 to MgO.
2FeCl3(aq) + 3MgO (s) 🡪 Fe2O3(s) + 3MgCl2(aq)
Hence the equation is balanced and we also identified the value of A, B, and C, which are 2, 3, and 3 respectively.
So A+B+C =8.