Quiet is a relative term. If you want to stand one foot from the tent, and hear absolutely nothing, in a dead quiet room, you are out of luck.
If you are OK with a slight air rushing sound, and a slight hum, that is doable.
The standard filter-fan-flex ducting will work well, if you run the fan on a speed controller, and throttle it down. I would also wrap the fan in fiberglass insulation to help dampen the noise.
A 4" fan should be more than enough for that size tent, assuming you don't need to run more than a few feet of ducting. Flex duct is a terrible flow impediment. Keep the run as straight as possible, and pull it taught to make it as smooth walled as possible.
A better method, in my experience is to think outside the box a little.
Larger carbon filter. Think Can66 size. Build a plenum box out of wood, or very strong cardboard. Fan goes on filter in box, pulling through filter, and blowing out of the box through a short length of duct. Stinky air is drawn through a duct from the tent, and into to side of the box.
This gets all of the crap out of the top of your tent, and lets you run a real carbon filter. You can put the plenum box anywhere nearby that you have space for it. With a 2x2 tent and a Can66, you will smell nothing. Nadda.
If you choose to go this route, I would suggest a 6" fan and speed controller.
For reference, I am running a Can33, a 4" tjerlund fan, and wayyyy too much ducting right now. Even badly restricted by the long duct run, I can slightly overdraw the filter, and get a whiff of the goods.
More carbon is a very good thing. I know it's not cheap, but you will appreciate the advice when you are not 8 weeks in, frying bacon and brewing coffee at 11pm because the little tiny filter from Amazon wasn't up to the task, and your place reeks of weed.
Wish could draw you a picture of the plenum box, but I'm using my phone atm.
Good luck, stay safe.
Regards, Kyle