Brenda thinks of a number y which she squares, then subtracts 5, next multiplies it by 4, subtracts 7, divides it by 3 and finally adds 6. Her answer is 9. What is the value of y?

Let's solve this step by step:

1. First, let's write down the operations Brenda does in the form of an equation. If y is the number Brenda thinks of, the operations she performs can be written as: ((y^2 - 5) * 4 - 7) / 3 + 6 = 9

2. Now, let's simplify this equation step by step:

   Subtract 6 from both sides: ((y^2 - 5) * 4 - 7) / 3 = 9 - 6 So, ((y^2 - 5) * 4 - 7) / 3 = 3

3. Multiply both sides by 3: (y^2 - 5) * 4 - 7 = 3 * 3 So, (y^2 - 5) * 4 - 7 = 9

4. Add 7 to both sides: (y^2 - 5) * 4 = 9 + 7 So, (y^2 - 5) * 4 = 16

5. Divide both sides by 4: y^2 - 5 = 16 / 4 So, y^2 - 5 = 4

6. Add 5 to both sides: y^2 = 4 + 5 So, y^2 = 9

7. Finally, take the square root of both sides to solve for y. Remember that the square root of a number can be positive or negative. So, y = sqrt(9) = 3 or y = -sqrt(9) = -3

So, the number Brenda thought of could be either 3 or -3.