Dismount any objects that are currently hanging on the wall bracket, and then remove the old mounting brackets. Use a Phillips-head screwdriver to remove the screws.
Open a new wall bracket kit. This kit will include a wall plate with drilled holes, a hanging bracket and screws. Depending on the type of bracket unit, it will have either two holes or four holes in the wall plate. Fit the wall plate on the wall and hold it over drilled holes in the wall. Insert the screws enclosed with the mounting kit through the holes of the wall plate. Use a Philips-head screwdriver to tighten the screws. Repeat until you fill all the wall plate holes with screws and the plate is completely secure to the wall.
Remove the current hanging bracket from the back of the object and replace it with the new one. Remove the old screws and attach your new hanging bracket and the new screws using the Philips-head screwdriver.