95 a6 with the 12v 2.8L

I feel stupid for asking this, but what is the big plastic box at the back of the engine that says V6 on it? I'm guessing it has to do with secondary air injection and the egr valve and all that jazz.

I only ask because my car's been throwing a code for the egr valve recently and I've read that sometimes a bunch of crud and stuff gets stuck up in there and stuff connected to it. So as I was doing my thermostat recently, I decided I might as well look at it.

Not only did I find out the passenger's side "tube" that goes into this thing from from the valve cover(I think) is broken in half, and was taped together... I also found out there was a bunch of liquid in there(as when I tipped it up all of the liquid fell on something hot and made lots of steam), along with a ton of crud. (Which I promptly washed out with brake clean.)

 

That's the Intake Air Housing (Box).

The breather hoses run into it indeed from the valve covers. If they get plugged with stuff could increase the crankcase pressure, leading to oil leaks, etc.
As you keep learning, you can even remove the valve covers and clean the vent chambers.