If your HQ is within 10 hexes ,counting terrain, of a level 10 city, it will have a supply level of 10. If you your HQ is 1 hex closer than the city value of a city that has a value less than 10, then the HQ will have a supply level of 8. Regarding your HQ with 6 supply, I can only guess that you are playing v1.04 and that another HQ was providing that supply level. I have not played in the east with v1.04 yet.
Gorski