$$2C_3H_8 + 7O_2 \rightarrow 6CO_2 + 8H_2O$$
According to the stoichiometry of the balanced chemical equation, 2 moles of C3H8 require 7 moles of O2 for complete combustion.
The molar mass of C3H8 is 44.1 g/mol, and the molar mass of O2 is 32.0 g/mol.
Therefore, the mass of O2 required to completely burn 96.6 g of C3H8 is:
$$96.6 \text{ g C}_3H_8 \times \frac{7 \text{ mol O}_2}{2 \text{ mol C}_3H_8} \times \frac{32.0 \text{ g O}_2}{\text{ mol O}_2} = \boxed{1042 \text{ g O}_2}$$
Therefore, 1042 grams of O2 are needed to completely burn 96.6 grams of C3H8.
