First create a shape to be cut through, cut away from, etc. This can be anything, even your model.
Now make the shape you want to cut away with. This shape can even be cut away to produce the desired shape also.
Place them in contact with each other, sticking through the desired faces.
Select the object you want to have a hole in. Now go to the rollout on the Command bar, scroll to Compound objects, and click the boolean button. Click pick operand B. Click the object you want to cut away with. In this case, the Box.
Now de-select the NESCESSARY vert's by holding Ctrl and clicking them so that only the non nescessary vert's are selected (if there are any).
Delete them. It should look something like this. The nescssary vert's should remain and the other will be gone as well as the faces Around them.
Use the create face tool after you convert your mesh to editale mesh and fill in those gaps!
Now flip the black ones to the side you prefer. and fill in the gap in the middle.
Now extrude or do whatever it was you did this in first place to do.
