Determine the correct set of coefficients to balance the chemical equation. __c6h6(l) + __o2(g)? __co2(g) + __h2o(g)

To balance this equation, first we should consider balancing C because it only presents in one reactant and one product.  Assuming the coefficient of C6H6 is 1, there are 6 C's in the reactant, so it generates 6CO2.  Then consider balancing H for the same reason. If the coefficient of C6H6 is 1, there are 6 H's in the reactant, so it generates 3H2O.
Now that the coefficient of the products are determined, we can balance O. There are 6*2=12 O's in CO2 and 3*1=3 O's in H2O.  So the total number of O in the products is 12+3 = 15.  O2 is the only reactant that contains O, so to balance the equation, the coefficient of O2 should be 15/2.
Now the equation looks like:
C6H6 + 15/2O2 ⇒ 6CO2 + 3H2O.
Times both sides of the equation by 2 results the final
2C6H6 + 15O2 ⇒ 12CO2 + 6H2O