You will not be able to merge two meshes together unless you have a vertex placed at the same location on both meshes, therefor you need to use either the split polygon tool or create edge loop tool or cut faces tool to create edges around the larger boxes at the location of the ends of the smaller boxes.
This will allow you to combine the two meshes and then merge the vertices,you can then delete the two internal faces that will not be seen.
Hope this is clear enough for you to understand.