I'd like to second electures motion on doing your own homework, talk with your teacher.
I also agree that from a practical standpoint, it's simpler to tie all the lights together with a pair of wires run either to one of the switches (typically one of the two 3-way switches, not the 4-way switches) or a junction box. However, your teacher may be looking for a little more imagination.
If you haven't seen it yet, look at some wiring diagrams of 3-way switching, then compare to 4-way switching. It's really just adding the 4-way (or two or three 4-ways) into the two travellers of the 3-ways.
Stick with it, it's the best trade around.