Hi Ariel G.,
From the periodic table we see 1 mol C = 12.0 g C; 1 mol Fe = 55.845 g; 1 mol O = 15.9994 g.
Therefore 1 mol Fe2O3 = 2*55.845 + 3*15.9994 = 159.688g or 159.7 g Fe2O3 rounded.
And from the reaction equation 3 mols C = 2 mols Fe2O3.
? grams Fe2O3 = 20.0 g C*(1 mol C/12.0 g C)*(2 mols Fe2O3/3 mols C)*(159.7 g Fe2O3/1 mol Fe2O3) = 177.4 g Fe2O3 needed to react with C.
I hope this helps, Joe.