Can a noun modify a gerund?
car repairing/door painting/room cleaning
It seems to me if it's possible it sounds ambiguous.
How is it going with your car repairing?
Does it mean that I repair cars and I am ask how good it is going? (your repairing of cars)
or
Does it mean that someone is repairing my car and I am asked how it is going? (your car's repairing)
While door painting, room cleaning and car repairing are all phrases I would consider valid English, I wouldn't use them in conversation unless I needed to specify context. For example, I would ask "How is it going with your car?" (repairing implied) or "How is it going with your repairing/repairs?" (car implied) instead of "How is it going with your car repairing?", and the context would be guessed by the listener.
It would be ambiguous whether you are saying the listener is repairing their own car, or someone else is repairing the listeners car if you said "How is it going with your car repairing?". If you wanted to imply they are fixing their own car, you would say "How is it going with your repairing/repairs?", as they are the one repairing. If you wanted to imply someone else is fixing their car, you would say "How is it going with your car?"
TLDR: It would be perfectly acceptable to use, but would sound a bit weird as you are overspecifying context
