I recently moved into an apartment with a very old Carrier thermostat (I think, too old to tell what it is).
The wiring of this current unit is as follows:
R
O
G1
Y
W2
C

I would like to exchange this unit for a Hunter programmable thermostat with the following terminals:
G
RC
Y
W
RH

This seems like a variation of a pretty common question, I would appreciate any help on this matter.

The new stat is not compatible with your heating/cooling system, since it appears to be a heat pump system. I get that is is a heat pump due to the O and W2 terminals, O being for a reversing valve, and W2 for auxiliary or emergency heat. Heat pumps will usually have electric heating elements built in to take over in the event the outdoor air does not have enough latent heat to draw from.

You may want to look more closely at your entire system to see if there are any labels or wiring diagrams that will prove my point.

Thanks for the information, I wasn't used to having a heat pump as I just moved from South Florida to North Carolina. I purchased an appropriate Honeywell thermostat and just finished the installation, it is working well so far.

Thanks again.