Explanation:

Correct Option is 1- 21

The divisibility by 11 rule states that if the difference between the sum of the digits at the odd and even places equals 0 or divisible by 11, then the number is divisible by 11.
The Sum of any two digits is not more than 18.
Calculation:
Sum of the digits at the odd places = (4 + 0 + 7) = 11
Sum of the digits at the even places = (a + 6 + b) = (a + b + 6)
Let the difference be 11k where K is an integer.
So,
11 - (a + b + 6) = 11k
Now, taking k = 0 we get,
11 - (a + b + 6) = 0
= (a + b) = 5
Now, we're taking k = -1 since (a + b) can't be negative and more than 18,
11 - (a + b + 6) = -11
= (a + b) = 16
Now, the sum of all the possible values of (a + b) = 5 + 16 = 21
The sum of all the possible values of (a + b), so that the number 4a067b is divisible by 11 is 21.