Well, you need to give us more to work with. I think I understand the problem. But we need to know more about what you know. The equation that you want to understand only holds for a certain type of system, not for any type of system. (For example, the equation would not apply to the adiabatic stirring of a glass of water.)
So, you first need to identify the type of system that you are working with (consult your text if necessary).
You will also need to know how to relate work to the change in energy of the system. There's a fundamental law of thermodynamics that will be of use here along with knowing what the term "adiabatic" means.
You will need to know the equation of state for the type of system you are dealing with. This will relate PV to the temperature.
Finally, you will need to know how to express the internal energy for the type of system you are dealing with in terms of the temperature and the integer i.
Once you have these ingredients, you can derive the equation you want to understand.