Reddit mentions of Phresh GL56701175 Inline Filter 6 in 500 CFM Science-lab-ph-Meters, 6 in | 500, Natural

Might work. Problem you will run into is that your single exhaust is going to pull from each tent evenly. So you'll have too much airflow in the veg tent, and too little in the flower. You can fight that using passive intake for the 2x4'. Or possibly just controlling how open the intakes are.

Make sure you are buying an inline filter. Which is more expensive than the usual ones. I run this Phresh model.

I do something similar, but with three 4x4' tents. Each has it's own 4" inline, and they all exhaust to a single 6" inline filter with a 6" inline fan hooked to it. It works well, but I do have to keep all the 4" fans running minimally, to keep air moving the right direction--this seemed easier than installing duct dampers.

Really, since you haven't purchased yet, I would run a 6" duct fan in the 3 x 20" tent, and a 4" inline fan hooked to a 4" carbon filter in the 2x4'. Skip the combined filter and fan. You don't really need a carbon filter for veg. That'll still let you exhaust to a single opening. Also, run the duct splitter as close to the outside opening as possible, to avoid one fan blowing back into the other tent.

That's a lot of money for a fan. You could always get a cheaper fan that moves more cfm and simply get a fan silencer. You would still save money at that rate and spend the rest on an enclosed hood or cool tube to help with temperature control.

Overall you're good.

Fan Silencer (out of stock at the moment, but cheaper): http://www.amazon.com/VenTech-VT-FS-6-Muffler-Silencer/dp/B00HWILBSS/ref=sr_1_3?ie=UTF8&qid=1450225496&sr=8-3&keywords=fan+silencer

Fan silencer (more expensive, but in stock): http://www.amazon.com/Phresh-701200-Silencer-4-Inch-12-Inch/dp/B007ZU5YQS/ref=sr_1_6?ie=UTF8&qid=1450225496&sr=8-6&keywords=fan+silencer

Hood Upgrade: http://www.amazon.com/Apollo-Horticulture-GLRLS24-Hydroponic-Reflector/dp/B00BMVK8HG/ref=sr_1_1?ie=UTF8&qid=1450225652&sr=8-1&keywords=air+cooled+hood

Fan and Carbon Scrubber Replacements: http://www.amazon.com/VenTech-VT-IF6-CF6-B-Controller/dp/B0051HDECS/ref=sr_1_1?ie=UTF8&qid=1450225799&sr=8-1&keywords=ventech+vt+if6

If you're going to be flowering in the tent, I would recommend lightproofing it, as well. Use only the ports in your tent for intake and cut some carbon filters to size. http://www.amazon.com/Carbon-Pre-Filter-38002-Activated-Sheets/dp/B00LXIWNT4/ref=sr_1_1?ie=UTF8&qid=1450225982&sr=8-1&keywords=carbon+filter+sheet

Your tent is a little expensive, too. If that's the one you have your heart set on, go for it. As an alternative, I suggest http://www.amazon.com/MILLIARD-Reflective-Hydroponic-Mylar-Window/dp/B00ETBDX14/ref=sr_1_1?ie=UTF8&qid=1450226158&sr=8-1&keywords=milliard+grow+tent

You will want a fan or two of some kind to circulate air inside the tent. 6 Inch clip fans are popular. I use a pair of 4 inch clip fans and a tower fan.

Make sure to look into a DIY Ona Bucket for smells. During flower it will stink up your room when you open the tent. Just turn the Ona bucket on a little before that and you're good. If you're really paranoid about smell, you can also get an inline carbon scrubber. They're pretty expensive and probably not necessary unless you pick some especially fragrant strains. http://www.amazon.com/Phresh-500-Inline-Filter-6-Inch/dp/B00CJIMUH2/ref=sr_1_1?ie=UTF8&qid=1450226390&sr=8-1&keywords=phresh+inline

That's my $.02, anyway. There are much more experienced growers here.

Phresh in-line filter 6in.

https://www.amazon.com/Phresh-Inline-Filter-500-CFM/dp/B00CJIMUH2/ref=mp_s_a_1_fkmrnull_4?keywords=phresh+inline+filter+6+in+500+cfm&qid=1558392827&s=gateway&sprefix=phresh+in&sr=8-4-fkmrnull

By FAR the best I’ve ever used... worth every dollar

Probably not the cheapest option, but you could use an inline filter outside of the tent, with just a couple inches of ducting routed inside the tent. I have one... it's quite a bit bulkier than the regular filters, but it does muffle fan noise a little.

Edit: and with an inline filter, if you ever decided to add a second tent, you could just add a duct wye, and exhaust both using a single fan & filter.

Those are super expensive because they have to clean it enough to be breathed directly. If you have the ability to vent outside you can use cheaper filters to remove the worst of the smoke and the reminants become a non issue. I do that with an inline carbon filter