To answer whether the equation is balanced or not we count the number of atoms on each side of the equation:
[tex]H_2+Fe_2O_3\rightarrow Fe^{\circ}+H_2O[/tex]Hydrogen: 2
Iron: 2 and 1
Oxygen: 3 and 1
As we can see both iron and oxygen are unbalanced.
We start by balancing th iron:
[tex]H_2+Fe_2O_3\operatorname{\rightarrow}2Fe^{\operatorname{\circ}}+H_2O[/tex]Now we have 2 atoms of iron on each side.
And then we proceed with oxygen:
[tex]3H_2+Fe_2O_3\operatorname{\rightarrow}2Fe^{\operatorname{\circ}}+3H_2O[/tex]So now we have the same number of each atom in both sides of the equation and it is balanced.