The principle behind balancing chemical equations is that, for any given element, the number of atoms that react must be equal to the number of atoms that are produced.
So, for your equation
Notice that neither of the elements involved in the reaction have the number of atoms that react balanced with the number of atoms that are produced.
The coefficients that must be added to the compounds must balance out the number of atoms that are on the reactants' side with the number of atoms that are on the products' side.
The actual balanced equation looks like this
Four atoms of iron react, four are produced. Likewise, 8 atoms of sulfur react, 8 are produced, and 22 atoms of oxygen react, 22 are produced.
For more info on how to balance chemical equations, check out this link