Installing Nest From HoneyWell T8575D Condo 8-Wire thermostats
After a series of testing, I am sure the Fan Common (Green #6) line is hooked to high voltage line of heater/cooler valve motor end switch, when the fan is switched to AUTO mode. Subsequently, Fan Common is connected to the Fan Low/Med/Hi input, depending on  which fan level the user sets the Honeywell thermostat. In this arrangement, the fan can start and stop in sync with the heater/cooler.
When the Fan Always On is set, the Fan Common (Green #6) is no longer connected to fan low(Red #7)/Med(Blue #8)/Hi(Brown #9). Instead one of the #7 #8 #9 is connected to the 24V power line and driven continuously regardless the state of heater/cooler.
As for the Nest Thermostat, it is able to sync turning on heater/cooler with driving one of the fan inputs (#7~#9 on my question diagram). There is no need to depend on the Fan Common Line (Green #6) to signal when to turn on a fan.
As such, the Fan Common Line can be left out in the connection to the Nest Thermostat.

This is how I test out functionality of the thermostats without the Fan Common Line

With the above arrangement, my thermostat works with heating, 3 levels of fan speed.