You want to find the coefficients a, b, c and ddsuch that
a(Fe2O3)+b(CO)→c(Fe)+d(CO2)
The idea is to make the number of each atomic species equal on the two sides of the equation equal. Then we have:
For iron: 2a=c
For oxygen: 3a+b=2d
For carbon: b=d
Oh, dear! Four unknowns but only three equations. Which implies multiple solutions. This might suggest a bad outcome. Or we could just arbitrarily set one of the variables to, say, one.
a=1. => c=2 (using the iron equation). And b=3,d=3 (using the value for a, and then solving the resulting oxygen and carbon equations).
Final result:
1(Fe2O3)+3(CO)→2(Fe)+3(CO2)