Combustion is the burning of a substance in the presence of oxygen. The results of combustion are carbon dioxide and water. So the general plan of the first part of the problem is to construct an equation with propane and oxygen on the left and carbon dioxide and water on the right. There is only one equation with propane in it, and that equation must be run in reverse in order to have propane as a reactant.
Since neither graphite nor hydrogen is a final product, both intermediates must be completely consumed in subsequent reactions. Graphite is consumed in equation (1). The coefficients must be tripled so that the graphite completely cancels.
Next, the hydrogen from the right side of equation (5) must be cancelled. Both equations (3) and (4) use hydrogen. However, the product of equation (3) is water, a
