The general rule of thumb is that for every foot of cantilever, you have to go back two feet into the structure. In your case, however, I would go the full four feet as you are carrying the roof load. Are your existing joists 2x12? I doubt it, but maybe they are. You need full access from above or below the joists, and doubled up cantilever joists to support the existing joists you will cut. You'll also need double and single joist hangers in the appropriate places.
As this thread unfolds, we'll gain more info to help you.