Question

Just need some clarification. I follow the even and odd part that in order to be even its 2k and odd is 2k+1. but where do they get the difference of 3 and 4?
Each integer n>11 can be written as the sum of two composite numbers.
Proof. Case 1: (n is even)
Since n is even, n=2kfor some k≥6.
Hence, n=2(k−3)+6
Case 2: (n is odd)
Since n is odd, n=2k+1for some k≥5.
n=2(k−4)+9 (The sum of two composites)