modular arithmetic - Is it possible to solve this congruency system?

I need help to determine if this congruency system can be solved and if it can be solved how do I do it:
$$\begin{cases}x\equiv2\text{ (mod $3$)}\\
x\equiv4\text{ (mod $6$)}\\

\end{cases}$$

I do know that from the system I obtain the following:

$$\begin{align}
x\equiv2\text{ (mod $3$)}\\
x\equiv4\text{ (mod $2$)}\\
x\equiv4\text{ (mod $3$)}\\
\end{align}$$

I do not know what to conclude from here. I think this system doesn't have solution, but if it is so how do I prove it.