Linear congruence solution confusion

Question

Why does: $4x \equiv 2 \bmod 6 $ have the solutions:

$x \equiv 2 \bmod 6 $ AND $x \equiv 5 \bmod 6 $

I understand why $x \equiv 2 \bmod 6 $ as: $4 \cdot 2 = 8$ which is $2 + (1 \cdot 6)$ :. $x \equiv 2 \bmod 6 $ but not sure why the second.

Answer 1

Consider the solutions of $$2x\equiv 1\ (\ mod \ 3\ )$$

Each solution of this equation is also a solution of the given equation and the answer is $x\equiv 2\ (\ mod\ 3\ )$, which gives the solutions $2,5,8,11...$

So, modulo $6$, the solutions are $2$ and $5$.