Summary

An insert for fixing an object to the wall. You can put a countersunk head screw into the wall the right depth, then slide your object on and there are no screw's visible from the front.
Small door hinge screws will be sufficient to hold the insert in.

To make the slot in the mating part you need a 16mm router bit or end mill. Then machine 20mm between centers about 8.5mm deep (the part is 8mm deep).

Suits any countersunk screw with a head < 9mm in diameter and a shank < 4 mm in diameter.

Print in ABS if you can. About 50% infill is good with 4 top and bottom layers.