**Solution:**

To find the values of A and b, we need to divide the given polynomials by their respective divisors and find the remainders.

Given polynomial 1: y³ + 2y² - 5ay - 7
Divisor: y - 1

Using long division method, we can divide the polynomial as follows:

y² + 3y - 2a - 5
y - 1 ) y³ + 2y² - 5ay - 7
- (y³ - y²)
-----------------
3y² - 5ay - 7
- (3y² - 3y )
-----------------
-2ay - 7
- (-2ay + 2a)
-----------------
-7 + 2a

From this division, we can see that the remainder is -7 + 2a. Therefore, A = -7 + 2a.

Given polynomial 2: y³ + ay² - 12y + 6
Divisor: y - 2

Using long division method, we can divide the polynomial as follows:

y² + 2ay + 4a - 4
y - 2 ) y³ + ay² - 12y + 6
- (y³ - 2y²)
-----------------
(2a + 2y² - 12y + 6)
- (2a + 4y)
-----------------
-16y + 6
- (-16y + 32)
-----------------
-26

From this division, we can see that the remainder is -26. Therefore, b = -26.

We are also given that 2A - b = 6. Substituting the values of A and b, we have:

2(-7 + 2a) - (-26) = 6
-14 + 4a + 26 = 6
4a + 12 = 6
4a = -6
a = -6/4
a = -3/2

Therefore, the value of a is -3/2.