Hexenary sounds more like the name for Base 6 to be honest. 16 is 6 more bases over Base 10, that is why 16 has been given the name Hexadecimal. Everyone knows 10 is Decimal, and adding on the #6 prefix “Hexa-” only means “6 more after …”. So …

“Hex(a)deci-mal = 16”
“6 (+ after) 10th-base = Base 16”

Here’s a summary for Base Names:
Binary = 2
Trinary = 3
Quadrenary = 4
Quinary = 5
Hexenary = 6
Septenary = 7
Octenary = 8
Novenary = 9
Decimal = 10
Unidecimal = 11
Biadecimal = 12
Triadecimal = 13
Quadradecimal = 14
Quindecimal = 15
Hexadecimal = 16

Hopefully you notice the logic now!

For simplicity’s sake, “10” remains as its own thing “an Even Number” even though it’s in #3’s position of Base 3, “11” remains as its own thing “an Odd Number” even though it’s in #4’s position of Base 3 and “12” remains as its own thing “an Even Number” even though it’s in #5’s position of Base 3. Thus it won’t matter what base number it is, while the odds “1,3,5,7,9” and evens “0,2,4,6,8” are sitting in the decimal number’s position. In Base2 the only odd number is 1 and the only even number is 0. In Base3 the only odd number is 1 no matter how big the # is (like 11, 101, 1101 or 101,101) and the even numbers are 2 & 0 (like 10, 12, 1010, or 20,010).

And F is just C upside down in their example.