Yes, you’re right, I got the boys’ names mixed up. It should have read:
K+7K/6=13K/6, so Kenny’s weight divided by 13K/6 is 6/13, that is 6/13(13K/6). Apologies.
It might be easier to consider an actual weight. Suppose Melvin weighs 98lb. Then Kenny weighs 6/7 of 98=84lb. Their combined weight is 182lb. Kenny’s weight compared to this total is 84/182=42/91=6/13. So Kenny’s weight is 6/13 their total weight.