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I dunno if you want something done by a non-FES'er, but here you go. A tutorial, made by Krevin, with a mug by Khorshid, and I have his permission to be posted here, and on the mainsite.
It's a tutorial to check and see how many colors are in a mug.
It's a good method but you could always just download a free simple program like Usenti, open the image, and look to the right to see how many colors there are. In addition you can just go Colors-Requantisize and type in "16" and it will make it 16 colors.