Is the Honeywell RTH9580WF thermostat compatible with the T874G1170 thermostat.

Both of these are for heat pumps, so I assume that you live in Florida or the southern US where heat pumps are used. How you wire it depends on whether the reversing valve is pulled in for cool (Florida) ("O" terminal) or whether the "B" terminal is used to pull in outside reversing valve for heat (Some more northerly states). You have "Y" for the main outside contactor, "G" for inside fan relay, "W-1, W-2", etc. for heat strips, and "C" for common and "R" for leg of control power that is switched to supply Y, G, O, (or B), and W. It's a five-minute job, just turn off the power first.