Transfer case
 

My 2000 Durango has two transfer cases that it uses. Np 231 Np 242
How can I find out which one it has without taking it off so I can order one online?

Ask online for that answer if you wish, but I'd want to know for sure. Crawl under and read the 2" round red tag on the back of the t-case near the speedo connector. The bottom of the stamped lines should be the model.
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If you have a full time 4wd position on the transfer case shifter, then you have the 242.