It will depend on the specific door and the opener. If the door is designed for low headroom, you should be able to put an 8' door with a 9' ceiling. I have installed 7' doors in garages with 8' ceilings. With the right track and opener, you need only 1' more than the door height.
I didn't have any room to spare, so I needed the full 12". Different doors and openers might fit in a few less inches. You need to contact the manufacturer.
If you are building a garage, give yourself a foot. It will go in 10" no problem with low headroom track. Once you get down to 6" you reach the point of diminishing returns because the door will not open to the full 8' anyway. And, the door will work like ****.
With the right track and a little know how, you can fit a door in just about any amount of headroom, but there is no point.
Just saw your other thread. You know, you can get doors in 3" increments in height. I would suggest a 7'6" high, given your 8'8" ceiling. 14" of headroom is enough for a 12" radius track and the door will open the whole way.
It can be done in 9foot but without low head room track you will probably will not get a opener on it. I have 8 foot doors with openers with a 116 inch ceiling hight with reg track.