Hello!
The balanced chemical equation for the rusting of iron is the following:
4 Fe + 3 O₂ → 2Fe₂O₃
The coefficients to balance the equation are 4,3,2. The fundament of this balance is the Law of Conservation of Mass. This Law states that matter is neither created nor destroyed in a chemical reaction, and in a chemical equation, the moles of each atom is conserved in both sides of the arrow. That means that if 4 Fe atoms are on the left side, 4 Fe atoms should be on the right side.
A suggestion for balancing equations is to start with metal atoms, continuing with non-metals, then hydrogen and lastly oxygen.
Have a nice day!