Start by balancing the hydrogen atoms. There are 9 on the reactants side and 2 on the products side. The least common multiple of 9 and 2 is 18, so the coefficient for C5H9O should be 2 and the coefficient for H2O should be 9.
Next, balance the carbon atoms. After giving C5H9O a coefficient of 2, there are 2*5, or 10 carbon atoms on the reactants side. There is only 1 carbon on the products side. The least common multiple of 1 and 10 is 10, so the coefficient of C5H9O remains as 2 and the coefficient for CO2 becomes 10.
Lastly, balance the oxygen atoms. With C5H9O having a coefficient of 2, there are 4 oxygen atoms on the reactants side. With CO2 having a coefficient of 10 and H2O having a coefficient of 9, there are 29 oxygen atoms on the products side. Here, you balance by changing only the coefficient of O2, which currently provides 2 oxygen atoms to the reactants side. 2 of the 29 oxygen atoms are covered by C5H9O, so the O2 needs to cover for the other 27. Every mole of O2 has 2 oxygen atoms, so the coefficient should be 27/2, or 13.5. We don't want decimals in the reaction, so multiply all of the coefficients by two. This gives the balance reaction:
4C5H9O + 27O2 --> 20CO2 + 18H2O
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