Merging shapes

Ok, I get the idea but recently my brain won’t compute. What is the best way to merge these two parts so that the backing on the left is retained while the cutouts on the right are retained.

@DragonDon Can’t really see from this one picture. Is the back of the left perpendiculat to the base surface of that body?
Is the height of the left body the same as that of the right body?
Would the merged body have these rounded corners as has the left body?
Dependingf on the answers, I’d start with the Intersect function (keep all originals). That would give you Several new bodies with which you can work