To solve this problem, we need to examine the relationship between the remainders and the divisors.

Given:
- x divided by y has a remainder of 6.
- a divided by b has a remainder of 9.

We can express these relationships as equations:
x = qy + 6 (where q is the quotient when x is divided by y)
a = pb + 9 (where p is the quotient when a is divided by b)

Let's first examine the relationship between x and y. Since x divided by y has a remainder of 6, we can rewrite the equation as:
x = qy + 6
Rearranging the equation, we have:
x - 6 = qy
This implies that the difference between x and 6 must be divisible by y.

Now, let's examine the relationship between a and b. Since a divided by b has a remainder of 9, we can rewrite the equation as:
a = pb + 9
Rearranging the equation, we have:
a - 9 = pb
This implies that the difference between a and 9 must be divisible by b.

We are asked to find a value that is NOT a possible value for y * b. In other words, we need to find a value that cannot be obtained by multiplying y and b.

To determine this, we can substitute different positive integer values for x, a, y, and b and check if the conditions are satisfied.

Let's start with option A: y * b = 21.
If y * b = 21, then the possible values for y and b could be (1, 21), (3, 7), or (7, 3). Let's check if any of these combinations satisfy the conditions.

For (1, 21):
x = qy + 6 = 7
a = pb + 9 = 30
Neither of these satisfies the conditions. Therefore, option A is a possible value for y * b.

Similarly, we can check options B, C, and D.

For option B: y * b = 20.
If y * b = 20, then the possible values for y and b could be (1, 20), (2, 10), or (4, 5).

For (1, 20):
x = qy + 6 = 7
a = pb + 9 = 18
Neither of these satisfies the conditions.

For (2, 10):
x = qy + 6 = 8
a = pb + 9 = 19
Neither of these satisfies the conditions.

For (4, 5):
x = qy + 6 = 10
a = pb + 9 = 18
Neither of these satisfies the conditions. Therefore, option B is a possible value for y * b.

Similarly, we can check options C and D.

For option C: y * b = 17.
If y * b = 17, then the possible values for y and b could be (1, 17) or (17, 1).

For (1, 17):
x = qy + 6 = 7
a = pb + 9 = 26
Neither of these satisfies the conditions.

For (17, 1):
x = qy + 6 = 23
a

Basic remainder policy
y>6 as remainder 6
same for b >9
so sum of y and b should be atleast greater than 6+9
so 15 can't be the answer