Pre-drill holes into the 2- by 4-inch board to use to attach it to the stucco wall.
Hold the board in position on the wall and use a pencil to mark the holes' location on the stucco wall. Set the board aside.
Drill holes for the anchor portion of the two-step masonry anchors fasteners. Drill the holes the exact size and depth recommended by the manufacturer of the anchors. The holes must be of the correct size in order for the anchors to secure the 2-by-4 to the wall.
Insert the anchor portion of the two-step masonry anchor into the pre-drilled hole.
Position the 2- by 4-inch board so its pre-drilled holes line up with the installed anchors. Drive the screws into the anchors using a manual or electric screwdriver.