Hanging down from about the junction of transmission and engine. Looks like the other end is up above the transmission.

Its one of your breathers - I recognise those little plastic caps. As its a longish hose it is the transfer case breather which normally sits up near the top of the transmission (looks like yours came loose). The transmission breather is very short and could not dangle down (at least on mine). You could cable tie it up hext to the tranny breather, or better yet - since it is there for the taking, extend it with a joiner and take it up to the firewall (that's one you won't have to do later if you get to the other five.

Thanks.

When you say extend it up to the firewall...why would you do that instead of just tying it up out of the way?

A number of people (at least in Oz) have extended the front diff, trans and xfer case breathers up high in the engine bay...I have mine finishing around the back of the fuel filter.
The rear diff can be extended and threaded up along the fuel filler tube to where the tank breather is situated.
This keeps everything above the water line.

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05 CRD Renegade

That mod is so you can take your Jeep swimming.

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Manure green 2005 CRD sport4x4, GDE Hot tune, Cat Gut, OE skids, Draw tight hitch, Duramax lift pump, 160K on multiple varieties of fuel, XM radio, Escort live with Redline, fog light mod, GPS, Icom IC7000 all band radio call sign KC9QPF, Grabber AT2s on Soft 8s, FIA grill blanket.

Once I worked on a piece of Waste Water Equipment that was set below ground to balance out the plant flow hydraulics. When the hurricanes came in, the area below ground would flood and water would go into the gearbox and cause problems. I removed the gearbox vent and placed it on a hose that put it above ground a few feet. The gear box never filled up with water again and the Engineer was impressed.

You all get one guess where I came up with the idea.

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2006 Pearl Green CRD
Magnaflow 2 1/2" Cat Back
KJ Extra Leg Room Brackets, Carter Lift Pump, V6 Airbox, ORM
Fuel cooler, Oil Separator, Progard 7
Gauges EGT Boost Trans Temp Oil Pres, Michelin LXT AT2 245 70 R16
7,000# Draw Tight hitch, PML EX Deep Trans Pan
Centrifuge, SunCoast, Transgo, RAM TCM, InMotion Stage 2
Wife's 99 TDI VW Beetle