For any integer n, 6|n if and only if 2|n and 3|n.
6|n is means n is divisible by 6.
So from the given statement we need to prove, if n is divisible by 6 if and only if n is divisibly by 2 and n is divisible by 3.
we know that 6 = 2 * 3
6k = (2*3)k where k = 1, 2, 3, 4, ….
So anything is multiple of 6 is divisible by both 2 and 3.
which means if n is divisible by 6 then it will definitely divisible by both 2 and 3.
Let assume n is divisible by both 2 and 3.
So n = 2m * 3r
n = 6 * m * r
So n is also divisible by 6.