Mark the location of the top edge of the hutch on the wall behind it with a pencil. Pull your hutch away from the wall so that you can access the space behind it.
Slide a stud finder along the wall where the hutch is located and mark the location of the two nearest wall studs with a pencil.
Center a safety bracket at each stud marking at the height of the back, top edge of the hutch. Use the pencil line from the first step as a guide. Drive the screws that were included with the safety brackets through the mounting holes into the wall studs using a screw gun.
Hold the furniture portion of the safety brackets in place against the back, top edge of the hutch so that they correspond to the positions of the wall portion of the brackets. Drill a hole through the mounting holes in the safety brackets into the back, top edge of the hutch using a drill equipped with a 1/16-inch bit. Drill the holes 3/8-inch deep.
Drive the screws that were included with the safety brackets through the mounting holes into the pre-drilled holes in the back, top edge of the hutch with a screw gun. Slide the hutch back against the wall. Slide the connector straps through both halves of each safety bracket and pull the ends through the slots in the straps to tighten them in the same way you would a wire tie.