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.
While doing this - it seems a little long winded. Rather than modeling my shape this way - would i be better infact to start with a single poly cube then extrude - this way i guess the edges would be merged anyway?
Bridge tool is easy just right click and select edges then select the edges you want to bridge and hit bridge,you might find that you have divisions and if that is the case either turn the divisons down to 0 in the chanel box after or set the divisions first in the option box of the tool.
Another way, and perhaps a little quicker would be to create a poly plane with 8x8 subdivisions. Then delete the faces you don't want. Then just select the object and extrude to the thickness you want. EDIT: SELECT ALL THE REMAINING FACES AND EXTRUDE IS WHAT I MEANT TO SAY.
As jsprogg mentioned, there are several different ways to model things and this is just another way.
Don't be satisfied with what you can do but rather strive to do the things you can't do!
SimplyMaya specialises in Maya tutorials. We offer over 1,000 individual Maya training videos, ranging from basic Maya tutorials through to intermediate Maya tutorials. Our tutorials are created by instructors with industry experience and are designed to get you up and running in Maya quickly without making it seem like hard work.