http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babyl...
But it seems unlikely as the origin of the Babylonian system cited. The 60 symbols are written in base 10; if it grew out of a culture that counted to twelve on their fingers, I'd expect to see five groups of twelve, not six groups of ten.
I can think of a more natural explanation. When I am counting something on my fingers (in the conventional way), I often want a way to store the tens digit. Perhaps the Babylonians did, too. That the tens digit is drawn as two groups of three is suggestive that whatever method they used stored a trinary and a binary state.
So, when I count off (palms up), I get to ten on the thumb of my right hand. It has a little more dexterity than my other fingers and can store more states. It's pretty straightforward to get to six by leaving it bent/straight and pointing out/up/in. It's natural to do while counting, too. (Bent and pointing in is a little uncomfortable if I want to use the other fingers, but then . . . you don't ever need to actually store 'six').