3" perfect wooden round hole in cabinet
Use a 3" hole saw or closest metric size on a drill. 3 inch hole saw

Use whatever tools you use to make a round hole in a door for a lock.

EDIT

What is on the other side of the cabinet where you want the hole? Is it open space or is it against a wall? I would say that pounding a nail repeatedly around a 3" diameter hole would likely damage the cabinet and maybe pull it apart at the joints. The right tool would be what used to be called a "keyhole saw" but is now usually called a "jab saw" (shown in the another answer, currently deleted). This tool is commonly used for drywall but can be used on other materials. You would drill a hole (say 3/8" or 1/2" diameter just inside the 3" circle and start sawing there.
Best jab saws