Find wood studs behind the stucco using an electronic stud finder. Mark the studs by making a vertical line using a pencil and ruler.
Drill a 1/4-inch pilot hole into the stud using a power drill and 1/4-inch drill bit.
Insert the 1/4-inch wall anchor into the pilot hole. Hammer the end of the wall anchor so it is flush with the wall.
Change the drill bit to a screwdriver head on the power drill. Insert the 4-inch screw into the pilot hole and anchor. Drill the screw into place.
Check with your manufacturer's directions for larger electronics, such as wall mounts for TVs. Additional screws may be required.
Hang the item on the wall. Mark the outline of the item with a pencil. Remove the item from the wall.
Rub the stucco with rough-grit sandpaper to make a level surface for the item to hang. Hang the item on the wall.