Basically a cleat is installed with good screws in the back into the studs of the wall.

I hope that helps. It is best to have a licensed and well experienced "cabinet contractor" construct properly and install under the laws of the state. In California we have stricter laws and guild lines due to our earthquakes. This way it prohibits the cabinets from falling during so called minor earthquakes. Also, these cabinets are not that large to create a large hazard in faltering.

Can you please tell me where the sofa and chair came from?