Turn on an electronic stud finder, and move it over the wall area centered behind where the bookcase will be located. The stud finder will beep when it passes over a wall stud. Measure to the left or right of the stud about 16 inches to find another stud. Mark both locations.
Measure the height of the wall security box you will use. Mark that measurement on the wall between the two wall stud locations you marked previously. The marks on the wall show the section of wall that needs to be removed between wall studs.
Create a hole in the middle of the wall area you want to remove. Use a drill or other tool to make the hole, which needs to be large enough for a drywall saw blade, jigsaw or sturdy utility knife. Use one of those devices to make a rectangular opening in the wall for the security box. Smooth the opening's edges as much as possible so they are straight lines.
Hold the security box with its door open in the wall opening. It helps to have a second set of hands do this task because you will use yours for another task. While the security box is inset in the wall, notice that the box's inside left and right sides have screw holes for attaching the box to wall studs with screws.
Mark on the wall studs where screws will attach the box to the wall studs. Use the box's side screw holes as guides for marking the wall studs. Remove the box from the wall opening.
Drill starter holes for the screws in the wall stud locations you marked. Hold the security box against the studs, place the screws through the box's side holes and attach the screws firmly into the wall studs.
Cover the edges of the wall opening with drywall tape, joint compound and paint. An option is to cover the opening's edges with wood trim molding, such as bull-nose or threshold molding.
Place the items you want to store in the security box, close the box's door and lock the box before moving the bookcase so it is in front of the security box.