If n+2C6n = 11, then n satisfies the equation:

Given, n+2C6n = 11
→ (n+2)(n+1)n(n-1)(n-2)(n-3) / 654321 = 11
→ (n+2)(n+1)n(n-1)(n-2)(n-3) / 720 = 11
→ (n+2)(n+1)n(n-1)(n-2)(n-3) = 7920
Let's try some values of n.
If n = 3, (5)(4)(3)(2)(1)(0) = 0
If n = 4, (6)(5)(4)(3)(2)(1) = 720
If n = 5, (7)(6)(5)(4)(3)(2) = 5040
If n = 6, (8)(7)(6)(5)(4)(3) = 20160
If n = 2, then (4)(3)(2)(1)(0)(-1) = 0
If n = 1, then (3)(2)(1)(0)(-1)(-2) = 0
If n = 0, then (2)(1)(0)(-1)(-2)(-3) = 0
If n = -1, then (1)(0)(-1)(-2)(-3)(-4) = 0
If n = -2, then (0)(-1)(-2)(-3)(-4)(-5) = 0
If n = 9, then (11)(10)(9)(8)(7)(6) = 332640
Let's assume there is a mistake in the question and it is meant to be:
(n+2)C(6,n) = 11
If n = 2, then (4)C(6,2) = 415 = 60
If n = 1, then (3)C(6,1) = 36 = 18
If n = 0, then (2)C(6,0) = 21 = 2
If n = 3, then (5)C(6,3) = 5*20 = 100
Let's try another approach:
Assume that the question was meant to be: n+2C6n = 11
Let's try n=2. Then we have: 2 + 2C62 = 2 + 15 = 17
Let's try n=1. Then we have: 1 + 2C61 = 1 + 12 = 13
Let's try n=0. Then we have: 0 + 2C60 = 2
If n=9, then 11C(6,9) is not possible since n must be less than or equal to 6.
It appears there's an error in the problem statement. The given equation doesn't seem solvable to find an integer n that satisfies it. There must be a typo in the question or the options.