Locate the studs in the wall with an electronic stud finder. This device indicates where a wall's studs are, with either a read-out display or a laser. Mark the spot with a pencil.
Mark off a spot at eye level on the wall. On average, this will be about 58 inches up from the floor. This is where the top of the cartouche should sit when it's hung.
Measure the distance from the top of the cartouche to its bracket. If the cartouche has a wire hanger, put your finger in the center of the hanger and pull it up. Measure from this point to the top of the piece.
Subtract the measurement from Step 3 from the eye-level mark on the wall and make a new mark. For example, if your Step 3 measurement is 2 inches, your new mark will be 2 inches below the eye-level mark. This is the spot where you'll hang the bracket for the cartouche.
Drill through the bracket mark with a masonry bit. Choose a bit that's slightly smaller than the width of the screw you'll be using, to provide a good bite for the screw.
Attach the hanging hardware to the wall with a drill or a cordless screwdriver. Line up the screw with the hole in the wall and drive it in. Make sure the bracket is flush with the wall and doesn't move from side to side. If it does, tighten the screws.
Center the cartouche on the bracket. Step back and make adjustments as necessary until the top of the cartouche is level. If the top is flat, you can use a level to make this step easier.