How to merge planes in blender 2.8?

Question

3D

How to connect copied (shift d) polygons to the main object?
As a result, after copying, I want to get the same recess on the right side as on the left side.

Answer 1

Make the side walls of the right recess clearly intersect with the front face of the large box (for example, by making the recess thicker or moving it slightly towards the front face). Then make the intersection of the objects and remove the extra edges.