I have cat back exhaust piping from a 92-95 civic hatch. Will it fit on a 96-00 hatch(asuming that have aftermarket headers and cat coverter on the 96-00)?

 

If you have aftermarket headerS, then probably not, if you had one header, maybe. Go find pics of the underbody of both cars and compare the piping. Or just rig it.

 

It might not work perfectly.
I have a 95 civic and got a 96 civic exhaust for dirt cheap.
The 96 exhaust has all the same bends but is about a foot longer. The flange was different also for some reason. 2 bolt compared to my 3 bolt 95. I chopped it off and put on an extra flange I had. With the extra piping I made a test pipe for the track.
Soooo. It can work if you add a short extension.