I always find it helpful to write down like this
Fe2O3 + CO --> Fe + CO2
2 Fe 1
1 c 1
4 o 2
So the first thing u have to double the O on the products side:
Fe2O3 + CO --> Fe + 2CO2
2 Fe 1
1 c 2
4 o 4
Now u have to double the C on the reactants side:
Fe2O3 + 2CO --> Fe + 2CO2
2 Fe 1
2 c 2
5 o 4
Now u have to change the O on the products side:
Fe2O3 + 2CO --> Fe + 3CO2
2 Fe 1
2 c 3
5 o 6
Now u have to change the O and C on the reactants side:
Fe2O3 + 3CO --> Fe + 3CO2
2 Fe 1
3 c 3
6 o 6
Finally, change the Fe on the products side
Fe2O3 + 3CO --> 2Fe + 3CO2
2 Fe 2
3 c 3
6 o 6