This equation is balanced by inspection. C3H8 is burned in an excess of oxygen. You will get CO2. Since C3H8 has 3 carbons, start by getting 3CO2 molecules on the product side.
C3H8 + O2 --> 3CO2
Note than you need 6 oxygen atoms so start with 3O2
C3H8 + 3O2 --> 3CO2
What happens to the Hydrogens? In a combustion reaction in oxygen the hydrogen is converted to H2O. Since you have 8H you will need 4 H2O on the product side.
C3H8 + 3O2 --> 3CO2 + 4H2O
Inspection reveals that the C and H are balanced but that we need 4 more O atoms on the reactant side
C3H8 + 5O2 --> 3 CO2 + 4H2O
it is now balanced: 3 carbons, 10 oxygen's and 8 hydrogens on both sides of the reaction.
