This answer is not correct. You have omitted a very important conversion factor...moles of silicon dioxide to moles of carbon. If you look closely at your conversion factors you will notice that you have moles of silicon dioxide in the numerator canceled out by moles of carbon in the denominator. This is how you solved the problem...

75.2 g SiO2 x mol SiO2/60 g SiO2 x 12.01 g C/ mol C =