It is desired to bring about a certain change in the state of a system by performing work on the system under adiabatic conditions.

By first law of thermodynamics we can write under adiabatic conditions $$dU = \delta W.$$   Since the work done is a path function to bring a certain internal energy obviously the work done depends upon path specified. this can be understood by taking the example of climbing up an hill in different ways the initial and end points are same but when he goes to climb the hill by using an rope he needs different amount of energy and if he goes by steps he needs different amount of energy (just for understanding). So, to bring a certain internal energy change one requires different amount of work when different paths are involved.