In the first part of the question, it asks for 1 solution, so I just made $2k+1=3l+2 $ and found that $k$ is $2$ and $l$ is $1$, so $x=5$. But what does that mean to find "all" solutions for this?
Use Chinese Remainder Theorem to conclude that the answer to the system of equations is $$x = 5 (mod 6)$$
There are more than one values which belong to the above mentioned congruence class. All those are solutions to your system of congruences.