In duodecimal, 10 is, indeed, the sum of 6+6. Add up 6+6 in your number system. The number you reach equals "10" in the number system I described.

Hexadecimal is a wonderful base, as it is the composite of 2 * 2 * 2 * 2.

But, it does not allow for even division by three or six, and that is a problem. The simplest regular polygon is an equilateral triangle. The angle of an equalateral triangle is 1/6th the angle of a complete circle. Hexadecimal cannot represent 1/6th of a circle without a fractional part. Geometry in hexadecimal would require something like the sexagesimal layer (360 degree circle) we stack on top of decimal to make it even remotely functional.

Duodecimal would not require that additional layer: The angle of a complete circle is "10". The equilateral triangle angle is "2". A right angle is "3". A straight line is "6".

With duodecimal, the unit circle is already metricated. Angles are metric. Time is metric.

Let me put it a different way: Our base is the product of 2 and a prime number. A 12-fingered alien who came across our decimal number system would think it about as useful and practical as we think of base-14, another number system with a base the product of 2 and a prime number.