How much weight can I lose, by walking 30 days, 8 hours a day?
I'm guessing you're overweight so let's assume you're a 180lb guy hiking with a pack in hilly country.
You're going to be burning over 500 calories an hour on the trail = at least 4000 per day.
During your 16 hours off the trail you'll be burning around 100 calories an hour = 1600 per day.
So your total calorie burn will be around 5000 - 6000 calories per day.
If you restrict your daily intake to 3500 calories a day (I've done this and found it workable) your daily deficit will be around 2000 calories per day.
Now, very roughly you need to burn 3500 calories to lose a lb of body fat. So you could expect to lose a bit over half a lb per day on your trek.
This was exactly my experience a few years ago when I started an alpine trek carrying around 20 lbs of excess fat and a 15 lb pack. After 30 days on the trail, including a couple of rest days, I'd lost around 15 lbs and was a few lbs short of my ideal weight.
Of course the actual figures will depend on your personal body-fat percentage, your metabolism and the height differentials on your walk, but this should give you a starting point.