We are remodeling our kitchen and moving the sink from a wall to an island in the middle of the kitchen. What distance from the rear of the cabinet do I need to have the sink drain pipe?

Will the pipe be coming up through the floor ? If so 4" from the back of the cabinet to the center of the pipe will work.

How will you vent the drain pipe?

Best Wishes

Are you referring to the vertical pipe(s) coming up through the floor or the horizontal pipe that the sink trap connects with? If the vertical pipe(s), keep them as close to the back as possible. The horizontal can be whatever you want.

i try to keep the pipe close to the back wall and over to the side as much as practical. those darn pullout faucets that people want. the hose has a weight on it to help it retract and it ALWAYS bumps the drain and/or hot cold pipes.
if you are building a short knee wall behind the cabinets, bring the drain and water pipes up in there.