Knowing the reactions between hydrogen gas and oxygen gas to form water is exothermic which would you say is greater: the average bond energies for hydrogen and oxygen or the bond energies for water? explain.

The answer would be: average bond energies for hydrogen and oxygen is greater than the bond energies for water

In the exothermic reaction, the reaction will release energy to the system. Since energy can't be created, the energy made from the reaction would be the result of a bond that broken minus bond that made. Since the reaction is exothermic which the total energy would be plus, the bond broken must provide more energy needed for the bond made. 
The equation for reaction that forms water would be: H2 + O2 = H2O
The bond broken in this reaction is H2 and O2 and their sum is greater than the bond made, which was the H2O bond.