Need to know what instrument they're using.

Puerto Rican Cuatro
 
Carl H. nailed it. On Wikipedia: Ten String Guitar , it describes the family. Clicking the Puerto Rico Cuatro link further down takes you to their web page with a photo of it.

A music store in North Carolina has one like it for $300 with a slightly different body style:

Reverb: 10-String Cittern Natural

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Reverb: Harry's Guitars photo.

Here is a Viola Guitar from Brazil:

Brazilian_10_String_Viola.jpg

Wikipedia photo.

It is a Puerto Rican Cuatro, but there are other variants, just like ukuleles have various different body shapes.
 
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