The sum of the coefficients is basically the total number of reacting molecules and products formed. However, you need to balance the equation first in order to reach the right value. For that, balance the aluminum with the oxygen and the product side.
This will give use 4 aluminum atoms reacting with 3 oxygen molecules to form 2 molecules of AL2O3. We can easily find the sum by adding all the molecules. 4+3+2=9. The sum of coefficients for this equation is 9. You can find the coefficient for other equations using this method as well. Simply balance the equation and then add the molecules on each side of the equation.