I've got a different(ial) situation...
 

So to start off I have a 1996 Miata that's bone stock basically and I love the car. I love miatas so much I decided to buy another one. After browsing craigslist I found a cool project. It was a 1992 Miata with a blown differential. I picked it up for $500 and immidiately met up with someone else to buy a differential. After getting my old differential out I realized the two were not the same. The one in the car had 4 bolt flanges on either side but the differential I bought, which came out of anther 1992 didn't have these. You can see straight through where the flanges are supposed to be. Is there a way to take the flanges off my old diff and put them onto my new one? If there isn't a way then what do I do?

You need to figure out what exactly you bought. Yes the flanges come out, you just pry them out. The fact that you can see through the diff, means that more than likely you got an LSD. Now was it for a 1.6 or a 1.8? Two different parts.

This may help

Differential Spotters Guide

the car has a 1.6

Yes, but 1.6 diffs blow like a cheap hooker, often. They are sometimes swapped for 1.8 diffs because they blow like a lesbian, not very often. They are also different sizes. The hooker diff is thinner because of the drugs. The lesbian has more meat on her because burly. So do you have a hooker or a lesbian diff?

you can see right though both. The one I bought is bigger for sure.