You would need to know the manufacturer and the part number. Then a search could be done with Google. Maybe that will produce an application.
Or, get the dimensions of the muffler;
outlet tube length
inlet tube length
To determine the inlet and outlet there usually is an arrow imprinted / stamped on the muffler indicating the flow direction. The inlet and outlet can be determined from that. Next, 'if' the manufacturer is known then go their site (if they have one) and if they offer product dimensions a determination can be made. Or, see if a catalog can be ordered. Possibly a very friendly parts store may be of help if they have a catalog.
Glancing at the image my best guess is it is a universal muffler that fits many cars. Universal mufflers generally just go by those dimensions mentioned earlier. Here is a link to DynoMax. http://www.dynomax.com/product-catalog At the upper right you will discover universal muffler. There are PDF files that show there different universal mufflers with dimensions.
Hopefully the muffler has the manufacturer name on it somewhere. Then you can be specific and discover the part number with a catalog like the DynoMax example. Universal mufflers don't usually have a make/model specific application reverse look-up (Part number to make/model). It is the individual using there prowess seeking finding a muffler for there purpose.
If I were wanting to sell that item on ebay for instance I would want to know;
The muffler type by brand
The Part number if possible
Those dimensions mentioned, or
The dimensions the muffler manufacturer uses
Next, at the main header feature I would list it something like this
New 'Manufacturer Name' Universal Muffler Part# XXXXXXXXX
Then include several pictures
Add a short description. For instance the one pictured looks to be polished. It may be stainless steel too.
For the price I would hope to find that at the manufacturer site firstly. Next, I would research ebay with a search to see where they are selling at and also what previous ones sold for.
I hope that helps . . .