When I see you next

When I see you next = The next time I meet you.

Note that it isn't actually a literal usage in this case. In the context of a classroom situation (for example), it means 'when the class meets again for a lesson'. If a teacher says "I'll explain it when I see you next", they mean 'in the next lesson'. If they happen to meet the students in a different context, such as in the cafeteria after the lesson, the teacher isn't suddenly going to start explaining the point there.