The correct answer is option 'A' - 9 birds.

Explanation:
Let's break down the information given in the question step by step.

1. The bird shooter said there were all sparrows but six. This means that there were six fewer than the total number of sparrows in the bag. Let's represent the number of sparrows in the bag as 'S'. So, the number of birds in the bag would be 'S - 6'.

2. The bird shooter also said there were all pigeons but six. This means that there were six fewer than the total number of pigeons in the bag. Let's represent the number of pigeons in the bag as 'P'. So, the number of birds in the bag would be 'P - 6'.

3. Similarly, the bird shooter said there were all ducks but six. This means that there were six fewer than the total number of ducks in the bag. Let's represent the number of ducks in the bag as 'D'. So, the number of birds in the bag would be 'D - 6'.

Now, according to the given information, the number of birds in the bag should be the same, regardless of whether they are sparrows, pigeons, or ducks. Therefore, we can equate the three expressions derived above:

S - 6 = P - 6 = D - 6

Since all three expressions are equal to the number of birds in the bag, we can say:

S - 6 = P - 6 = D - 6 = Total number of birds in the bag

Now, if all three expressions are equal, then we can say:

S - 6 = P - 6
S = P

Similarly,

S - 6 = D - 6
S = D

Therefore, we can conclude that the number of sparrows, pigeons, and ducks in the bag is the same.

Now, let's substitute the value of 'S' in any of the three expressions:

S - 6 = Total number of birds in the bag
S = Total number of birds in the bag + 6

But we know that S = P = D. So,

Total number of birds in the bag + 6 = Total number of birds in the bag

Simplifying the equation, we get:

6 = 0

This equation is not possible as it leads to a contradiction. Hence, there is no solution to this problem.

Therefore, the correct answer is option 'A' - 9 birds.