My Honeywell TH6220 thermostat quit working and I purchased a Honeywell RTH6400 Thermostat. The old thermostat has a Y2 wire. What should I do with it on the RTH6400? It only has G, W (O/B) Y, R, and RC. The installation guide says nothing about what to do with Y2. Any help is appreciated.

Take the thermostat back and get the right one...
Does your condensing unit have a two stage compressor or a high and low? If not the y2 is not needed.
What kind of unit and seer do you have?

The 6400 is a simpler thermostat that doesn't support the extra heating/cooling stages the 6220 did. Take it back and find something that will support the same capabilities.

If not sure what thermostat to go with just post back.

Try the honeywell pro 6000, it is a 2 stage heat, 2 stage cool stat. It will work with single stage or two stage systems.