Notice that there is a 3-conductor cable coming into the first box, then a 4-conductor cable going from left box to right box, then a 3-conductor cable going from the right box to the load. Now for wiring, lets assume you're looking at the switch just like it shows. The Left Box: The lower left screw is the common and gets the black wire from the source 3-cond. The upper left screw gets the black wire from the right box 4-cond. The upper right screw gets the red wire from the right box 4-cond. The white wires tie together with a wire nut.
Three-way switches require a three-wire cable: the power wire, the neutral wire, and the traveller or switch wire. The cable should also have a ground wire, or a total of four wires in the cable. The system also requires three-way switches. The switches are wider than regular single-pole switches and they have three terminal screws on the side sometimes back of the switch housing. Two terminals will be on one side of the switch housing; one terminal on the other side.
No longer allowed after NEC if no neutral wire in switch boxes. Line voltage enters the first 3- way switch outlet box, light fixture is located between switch boxes. There is no standard for wire colors on 3- way switch travelers.