How would i screw this into the cabinet instead of the electrical box?

I want to screw this into the cabinet instead of the electrical box and then add a faceplate. How would i go about this? Im not able to connect to the electrical box at all from the wood side.

I want to screw this into the cabinet instead of the electrical box and then add a faceplate. How would i go about this? Im not able to connect to the electrical box at all from the wood side.