If the only choice is between 6 miles/day and 8 miles/day, and the target is a 35:00 10K, then 8 is always better than 6, like J.O. said, because it builds better endurance, regardless of sex, age, mileage, previous history, etc. If you are currently running 40 mpw, a typical progression, to get to the next level, is to bump that up to 70 mpw.
The only risk is injury, if you are not ready.
Even better is to mix it up with variety of distances, paces, and terrains. Run 6 miles fast pace on the road one day, 8 miles medium pace over undulating hills another, 10 miles slow on another, 1 hour fartlek on another, short recovery another, etc.
I would add a couple questions to the list above:
- What is your competition schedule between now and summer?
- When do you need to peak?
- Do you want a periodic/phased approach to training? How many weeks of "base training" in winter?
For more detailed practical advice, better to read something like Daniels Running Formula, or go to Lydiard Foundation website, than to ask random questions (and get random non-comprehensive answers) in this forum.