Measure the height and width of the back of the vanity. Use these measurements to choose a position for the vanity on the wall where the stub-out pipe and water supply valves sit, marking an outline on the wall of the back of the vanity.
Draw the sketch on the wall of the vanity cabinet so the edges sit at least half an inch from any other objects, such as a corner, providing sufficient overhang for the vanity top. Measure the distance from the edges of the sketch to the center of the stub-out pipe and water supply valves.
Mark the position of the center of the stub-out and water supply valves on the backside of the vanity. Choose hole saw attachments that are larger than the stub-out and valve assemblies to make the corresponding holes in the cabinet.
Place the center of the hole saw on the marking for the center of each of the pipes. Turn on the drill to cut the holes in the back of the cabinet. Slide the cabinet over to the area you marked on the wall, lining the holes up with the stub-out and valve assemblies.