It is standard to write,

Note, the we can factor 6 as 2 times 3.

Where 2 and 3 are relatively prime.

Thus, it is equivalent to saying the system of congruences is satisfied:

(1)

(2)

The first congruence is true because consider cases when is even or odd. It is true in both of them.

The second congruence is true by Fermat's little theorem.