Explanation:

Let’s break this one down step by step:

- We’ve got: 2a + b = 10 … (1)

- Also, 2ab = 9 … (2)

- And we know: 2a > b

Start with equation (1):

- Let’s solve for b: b = 10 - 2a

Now, plug that into equation (2):

- 2a * (10 - 2a) = 9

- 20a - 4a² = 9

- 4a² - 20a + 9 = 0

Let’s use the quadratic formula:

- a = [20 ± v(400 - 144)] / 8

- v256 = 16

- a = (20 + 16)/8 = 36/8 = 4.5

- a = (20 - 16)/8 = 4/8 = 0.5

Plug back for b:

- If a = 4.5, b = 10 - 2*4.5 = 1

- If a = 0.5, b = 10 - 2*0.5 = 9

Check 2a > b:

- If a = 4.5, 2a = 9 > b = 1 ?

- If a = 0.5, 2a = 1 < b = 9 ?

So, the valid solution is a = 4.5, b = 1.

Now: 2a - b = 9 - 1 = 8

Options recap:

1) 12

2) 6

3) 8

4) 10

The correct answer is:

8 (Option 3)