On an 8-11% grade I probably want to be in a gear ratio near 1:1. The most used gear on my mountain bike is 32 in the back and 33 (middle) in the front. It's possible to do it in a harder gear (and you will go faster as a result) but it takes time to build up the strength and endurance to push higher gears. If you are starting out, use an easier gear, spin the pedals faster, and move slower. If you are spinning really slow or standing up to pedal you are going to tire yourself out because you are using strength not aerobic endurance for that. Find a route that lets you go slow, and you can climb almost any grade. I regularly do a ride that has a 1/2 mile dirt/gravel section that's a 25% grade most of the way up. It's not that bad in the lowest gear, but I'm barely moving faster than someone walking.
You can probably change the gearing on your bike if you need to (and I would recommend it if you can't make it up the hill easily. Typical road bike gearing is stupid for most people). An easy way would be to change out one or more of the front chainrings. 22-33-44 is standard for mountain bikes, but road bikes have bigger gears. If you made one or more of them smaller everything would still work as long as you don't have a big transition from one to another (don't do a 22-42-52 setup, for example).
You could also change out the back cassette. 11-32 is standard for mountain bikes, but road bikes might have 11-28 or worse 11-22. If you get a cassette with a bigger lowest gear you might need to change some other things. The chain will have to be made longer (replace it with a new chain and set it up to be long enough. New chains are always too long, but they are shortened to fit the bike when they are installed), and you might need a rear derailleur with a longer cage to maintain chain tension over a wider range of gears. The new cassette needs to be the same number of speeds as the old one or your shifters won't work. Usually cassettes are replaced as one piece and you can't change out individual gears like you might do for the front chainrings.
Mountain bike and road bike parts often work interchangeably, but not always, so if you change things you should check with someone to make sure everything will still work. There's not really any inherent difference a lot of times, and you could have a road bike with a full mountain bike drivetrain if you wanted. The only downside to that is your top speed would be limited to less than about 45mph, and you wouldn't have as many gear choices at road cruising speeds.