I am trying to install my new rancho rear shocks and the spinning lockwasher pulled on a hose and pulled it down from where it was mounted. I need to know what this hose does. It attaches to the brake lines attached to the axle. I have attached a picture of both ends of the hose.

 

That needs to be clipped up to the frame somewhere high. Not sure if its a vent of some sort or what it does exactly maybe some one else can chime in.

 

it "appears" to be the breather for the rear end, I could be wrong. You'll want that end up high somewhere, especially if you're launching boats, etc.

 

That's the breather hose for the rear axle, make sure to squeeze the clip before putting back on the rail of the box just above the axle or you will find it dragging again later.

 

+1 that's what it is alright.

 

yup thats the vent line for the rear end, put ti up high and away from anywhere it will get submerged in water.

 

What they said. Breather/vent for diffrential housing. Clips up high somewhere, your choice.