We have 2 Fe atoms on the left side of the equation and only 1 on the right side. To balance this, we put a 2 in front of Fe on the right side. Now, our equation looks like this:
$\mathrm{Fe}_{2} \mathrm{O}_{3}+\mathrm{C} \rightarrow 2\mathrm{Fe}+\mathrm{CO}_{2}$
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