which xbox 360 do i have

With the serial number itself I do not believe there is a way.

If the sticker with the serial number is still in tact on the console there should be a model type.

There were quite a few different model types.

You had the original

the 360 S

the 360 E

Was there a particular reason that you were needing the model type?

With a picture or something we wouldn't be able to tell

Hi Claudia2110!

If you know the Microsoft account associated with your son's Xbox profile, you can go to account.microsoft.com/devices to view the console's details. You'll see a tile
with a picture of the device, the device's configured name, and then the name of what type of device it is.

Late 2009 120GB black Elite and my missus has a 120GB red Resi 5 LE.

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Also, still have my 20GB Halo 3 console.

Xbox 360 320GB Gears 3 Edition