Ah - I see now.
If you use the SUVAT equation, and write down an expression for the change in kinetic energy, you will see that the initial and final velocities will be eliminated, allowing you to work out directly the average force by simply dividing the energy loss by distance falling. This is just equivalent to work done = force x distance.
The problem is how to combine the loss of KE with loss of energy to atmosphere. This is really the crux of the question, and I don't want to spoil it for you, but try to draw a force diagram with air resistance (opposing motion) and weight (opposite to air resistance) and think about which way the resultant force will point. Once you have done that, you should be able to assign the forces calculated from the two energy changes you have been given, and the remaining term is just the weight = mg. Rearrange the expression to get average g.