While this is technically correct, this step is completely unnecessary since it adds no new information. We already know that p is divisible by 2 and by 3, and since p=3n for some integer n it immediately becomes clear than n must be divisible by 2. In other words, n being divisible by 2 is technically given (no need to plug in p=3n to figure it out). If n wasn't divisible by 2, what would it say about p=3n?