there are literally an infinite number of ways to answer this... since it has been so long, I'll give some examples:
simplest (in my opinion) is just telling the number of letters in the number (word) the guard says (twelve = 6, six = 3, ten =
3)
a more complex example (just one of a an infinite number) would be to give the digit which when put onto the end of the number the guard says (to form one number) would give a number which is a multiple of 9 -- for example:
12 , 6 = 126 which is a multiple of 9 (9*14=126)
6, 3 = 63 (9*7 = 63)
10 ,
8 = 108 (9*12 = 108)
or another:
if guard gives a two digit number, you add the digits together and multiply by 2 (1+2=3 -- 3*2 =6) or if the guard gives a one digit number you simply divide it by 2 (6/2=3) GIVING answer
2 (1+0=1 -- 1*2 = 2)
again, the list is literally endless ... add your own? (bonus points if it does not just include numbers LOL)
(for example: 10 =
6 because... (keep with me here) the guards have a list of animals put together, one animal for each letter of the alphabet. the guard will give a number representing which letter the animal starts with, then the reply is the number of letters in the animal's name -- 12 = L ... L = LIZARD which has 6 letters, so 12=6 ... AND 6 = F ... F = FOX which has 3 letters AND 10 = J ... J = JAGUAR, which has 6 letters) ... sure it's overly complicated, but perfectly fine with the examples given LOL (yeah, I like riddles and puzzles

)