To solve this question, we need to find the values of 'a' and 'b' that satisfy the given conditions of the quadratic equation. Let's break down the steps:

Step 1: Identify the quadratic equation
The quadratic equation given in the question is ax^2 + 3x + 2b = 0.

Step 2: Use the sum and product of roots formula
The sum and product of the roots of a quadratic equation can be found using the formulas:

Sum of roots = -b/a
Product of roots = c/a

In this case, the sum of roots is given as -6 and the product of roots is also given as -6. So, we can set up the following equations:

-6 = -3/a (Equation 1)
-6 = 2b/a (Equation 2)

Step 3: Solve the equations simultaneously
To solve the equations simultaneously, we can use substitution. Rearrange Equation 1 to isolate 'a':

-3/a = -6
a = -3/-6
a = 1/2

Substitute this value of 'a' into Equation 2:

-6 = 2b/(1/2)
-6 = 4b
b = -6/4
b = -3/2

So, the values of 'a' and 'b' that satisfy the given conditions are a = 1/2 and b = -3/2.

Step 4: Simplify the values
To simplify the values of 'a' and 'b', we can multiply both numerator and denominator by 2:

a = 1/2 * 2/2 = 2/4 = 1/2
b = -3/2 * 2/2 = -6/4 = -3/2

So, the simplified values of 'a' and 'b' are a = 1/2 and b = -3/2.

Step 5: Write the final answer
The final answer is the values of 'a' and 'b', which are a = 1/2 and b = -3/2. However, the answer choices are given in integer form, so we need to convert the values to integers. In this case, the correct answer is option 'B' (-1), as it is the closest integer approximation to -3/2.