The correct solution for this problem is choice (a).
Let's break down the each step of solving this problem:
1. First, we have a value for 'a', which is a = -3.
2. Secondly, we calculate the value for 6a. This means we should multiply the value of 'a' by 6. When you multiply -3 (the value of 'a') by 6, you will get -18. So, 6a = -18.
3. On the next step, we need to calculate the value for 8b. This means we are required to multiply the value of 'b' by 8. Since 'b' equals 9, after multiplying it by 8, we get a result of 72. So, 8b = 72.
4. Then, we calculate the absolute value of 'a', which is representing the positive value of 'a'. The absolute value of a negative number makes the number positive, so the absolute value of -3 is 3. Therefore, |a| = 3.
5. And lastly, we find the absolute value of 'a - b'. When we subtract 'b' from 'a' we get -12 as a result (-3 - 9 = -12), and the absolute value of -12 is 12. Hence, |a - b| = 12.
So, after all calculations, we have:
a = -3, 6a = -18, 8b = 72, |a| = 3, |a - b| = 12.
This is fully according to the choice (a), therefore the answer is (a).