3 way switches with switch load at each end
You have two totally separate 3-way switch complexes, right next to each other. They are totally separate and must be isolated from each other.  Each uses a different wiring diagram.   It will be VERY confusing.  

In cases like this, I rely on colored tape. Get a 5-pack of colored tape and get ready to mark some wires.   The first rule of marking wires is mark both ends of the wire at the same time.  The second rule is when you mark a wire, that is its color now.  The third rule is you cannot mark a colored wire white, i.e. A colored wire cannot be made a neutral. 

I prefer black for supply hot, red for switched hot to a lamp, yellow for a set of travelers (they are interchangeable), and blue for a second set of travelers.

On each of the 14/2 spurs to the lamp, mark the black wire with RED tape. It is now a red wire. 

On your 14/3 cables between switch boxes:


One cable gets wire colors of yellow, yellow and red.  Yes, 2 wires with the same color. 
The other gets colors blue, blue, white.  


In the right box, pigtail 2 wires off the black supply.  They each go to the common (black screw) on a 3-way.  

In the right box, the "traveler" terminals (brass screws) on the 3-ways:  one 3-way gets both yellow wires.  The other 3-way gets both blue wires.  

In the left box, one 3-way gets red on its common screw and both yellows on its two traveler screws (brass). That 3-way is done.  

Also in the left box, land both blues on the traveler screws of the other 3-way.  

Nut all white wires together in both boxes.  

Nut both red wires together in the right box.  That box should be done. 

In the other box, one red wire still dangles, and one 3-way screw is unused.   Use it for that.  

And we're done. Whew!