I'm trying to change my old Honeywell thermostat (which looks like T8400C) for programmable Hunter (model 44155C). Old one was connected to Hail Quiet Comfort II two stage gas furnace (on the second floor) and air conditioner (outside of the house). It has 6 wires connected to Honeywell: G (green), C (blue), R (red), W1 (white), Y (yellow) and W2 (brown). Hunter model supports only up to 5-wire heat/cool system, which marked RH, RC, G, Y/O, W/B and Y1. Honeywell is not battery operated, while Hunter does have a battery. Could anybody help me with wiring correspondence, please?

The thermostat you purchased will not work, it's a 2 stage cool single stage heat, you need a 2 stage heat single stage cool or a multi stage thermostat.