Two points, $A$ and $B$, are located above the surface of a mirror. The direct distance from point $A$ to the mirror is $y$ cm, and the direct distance from point $B$ to the mirror is $3$ cm. A light ray from point $A$ is reflected on the mirror and covers a total distance of $12$ cm to travel to point $B$. If the distance between points $A$ and $B$ is $6$ cm, find the value of $y$.