How do you balance #Fe_2O_3 + H_2 -> Fe + H_2O#?
By the usual process of stoichiometry: garbage in must equal garbage out.
Is this reaction balanced? Do not trust my arithmetic! Industrial production of iron and steel would utilize carbon monoxide (from coke) as the reductant. The use of dihydrogen as the reductant is certainly feasible (given a sufficiently high temperature), but the process would be supremely uneconomic.