You can use any frame of reference which you want. But it is best to look for a frame which makes the problem easier to solve.
Using a frame of reference fixed in the right-hand wedge is no more difficult than one fixed in the left-hand wedge. In this frame the left wedge moves left with speed $3u$ and the cylinder moves vertically downward with speed $v$.
In time $t$ the wedge moves left by distance $x=3ut$. The point of contact with the cylinder moves down by distance $y$ such that
The vertical speed of the cylinder in this frame is
Transforming back into the laboratory frame, the cylinder has velocity $2u$ horizontally to the right and $\sqrt3u$ vertically down. Using Pythagoras' Theorem the resultant velocity is