The correct option is
A 12Fe2O3(s)+C(s)→Fe(s)+CO2(g)
Number of iron(Fe) atoms: 2 on LHS, 1 on RHS
Number of carbon(C) atoms: 1 on the LHS, 1 on RHS
Number of oxygen (O) atoms: 3 on the LHS, 2 on the RHS
Since we have an odd number of oxygens, we should balance,
Multiply by 2
2Fe2O3(s)+C(s)→Fe(s)+CO2(g)
Lets balance the oxygen on the other side by multiplying by 3
2Fe2O3(s)+C(s)→Fe(s)+3CO2(g)
Balancing the carbon by multiplying by 3 on LHS
2Fe2O3(s)+3C(s)→Fe(s)+3CO2(g)
Finally, balance the iron by multiplying by 4 on LHS
2Fe2O3(s)+3C(s)→4Fe(s)+3CO2(g)
The sum of the coefficients is 2+3+4+3=12