Speaker wall plate wiring
The terminals on the back side of that speaker connection adapter are meant to be used with a type of crimp on terminal such as those pictured below:



(Picture source - https://www.arc-components.com/2-001-34-pack-of-100-durite-coloured-crimp-terminal-480mm-push-on-red.html)

These come in various sizes, colors and styles. Some types are covered with insulation and others like above are insulated only in the crimp area. The terminal is pushed onto the short stripped end of the in wall wire then crimped in place using a special tool designed for this purpose. The terminal is then pushed onto the flat ends of the terminals on the back side of that mount plate.

You can source these from many places including your local auto parts store.