Explanation

The combination formula is:

nCr = n! / (r!(n-r)!)

Given that nC12 = nC6, we can equate the two expressions:

n! / (12!(n-12)!) = n! / (6!(n-6)!)

Simplifying the equation, we get:

12!(n-12)! = 6!(n-6)!

Since 12! = 12 × 11 × 10 × 9 × 8 × 7 × 6!, we can cancel out the 6! terms:

12 × 11 × 10 × 9 × 8 × 7 = (n-6)(n-7)(n-8)(n-9)(n-10)(n-11)

This equation is true when n = 18.

Therefore, the correct answer is 18.