You can actually count to 12 on your fingers using one hand. Use the thumb as a pointer, then for each of your other fingers you have three joints. So 3*4=12.
It's hard to actually count using more than 4 bits/hand though. The quickest methods that require the least dexterity are those that count the knuckles (which are actually used in some counting traditions, unlike binary finger-counting).
Let’s go hexadecimal all the way.