Think of it like balancing a financial ledger: three oxygen atoms bring a total debt of $-6$, which must be offset evenly by two iron assets, meaning each iron represents $+3$.

Remember 'O is $-2$' to quickly solve transition metal oxidation numbers in oxides.

To determine the oxidation state, apply the algebraic rule where the sum of oxidation numbers in a neutral compound equals zero. For $Fe_2O_3$, let the oxidation state of iron be $x$, yielding the equation $2x + 3(-2) = 0$, which solves to $x = +3$.

Memorize common oxidation states of standard elements like oxygen and alkali metals to quickly solve complex redox and transition metal problems.