Intrinsic reinforcement (or intrinsic anything) is not something any of us can do to or for another person. It's something that happens inside a person (child or adult) that makes him or her want to continue the actions that made him or her feel good.
Here's an example:
My grandson (a high school freshman) gets zeroes on 3 assignments. These zeroes indicate that he didn't turn in those assignments. He insists that he did turn them in, but his mom says he must do whatever it takes to get it all straightened out with his teacher. She makes no other effort to help him get his grades straightened out because she wants him to learn to fend for himself and be happy with the results.
1. If he goes to the teacher and is able to prove that he turned those assignments in, and if the teacher accepts his proof and corrects those grades, he will have a feeling of accomplishment -- certainly for his mom, but mostly for himself.
2. If he does nothing and allows those three zeroes to bring his overall grade down, it will adversely affect his semester grade, even if he does well on his final exam. He will undoubtedly feel like kicking himself for not taking steps to get his grades taken care of before exams.
Either way, his mom and dad love him. But which actions -- #1 or #2 -- will empower him and help him know how to deal with similar situations in the future?
Now ... what scenario can you describe for a younger child?