Kenny is close to his parents and feels comfortable going to them about his problems. Kenny offends Rufus, his only friend, and unsuccessfully tries to apologize to him. Momma can tell something is bothering Kenny, and she advises him to try apologizing again and give Rufus more time to forgive him. Then Momma goes to Rufus and talks to him on Kenny's behalf, and the two boys are able to make up. Now, what do you think she might have said to him?
Stop and consider the type of person Momma is -- she's kind, sensitive, and a good parent. I'm sure she first asks how Rufus feels and listens to him. I would guess she then gets Rufus to see things from Kenny's perspective so he can understand how badly Kenny feels and why Kenny acted the way he did. Once Momma is able to get Rufus to put everything into perspective, he is able to accept Kenny's apology and forgive him.