Wiring two 3-way switches with 2 light fixtures and 1 outlet
Your teacher is wrong.  You can't do that.

Between the lamps you need four wires: 


Two travelers, since they need to go past  the lamps
A switched-hot, since both lamps need switched-hot
A neutral, since both lamps need neutral


That's four wires plus ground, all of which are part of the same subcircuit. 

Since the four wires are related and part of the same subcircuit, they must be part of the same cable.  Your instructor plans to use two 14/2 cables to provide the 4 conductors.  That is a violation of NEC 300.3(b), all related wires must be in the same cable.  Why? Eddy current heating and vibration causing fatigue breaks, we're dealing with AC here. 

He also forgot neutral to the switch box

His installation violates 404.2(c), which requires neutral come to every switch box.  That is a NEC 2011 requirement to support "smart switches". 

So let's reboot this deal

Assuming these lights and switches are ~18" apart, this will not work with the segments of wire he specified.   However, this is how you do it.  I chose colors by function (red=switched hot, yellow=2 travelers).  Common cables may not come in those colors; whatever, that's what colored tape is for. 

 

This diagram omits ground because it doesn't require any thinking and it just clutters up the diagram.

Note how you will have a single, /3 cable between the switches.  The /3 cable only needs to go between the switches. 

Don't do one of the stupidest things you can do in a 3-way circuit, running the messengers through the lamp boxes for no reason whatsoever.  Having the /3 cable stop at the lamps is useless, and far worse, it obliges you to have 3 splices of 2 wires each, which adds a bunch of box fill (12-13.5 cubic inches) to a standard octagon box that's already way too small for that.  It is simply insane to do this. 

Once you've reached the far switch, you double back on a different route,  with /2 cable to the lamps.  

This assures we comply with 300.3b (all related wires together in same cable), avoids using expensive 14/4 cable, and complies with 404.2c (neutrals at switches).