Let's solve the two absolute value problems in the image:

(a) $|-6 + 9|$

1. First, perform the operation inside the absolute value brackets: $-6 + 9 = 3$
2. Now, apply the absolute value, which is the distance of a number from zero on the number line (i.e., always positive): $|3| = 3$

So, the result of $|-6 + 9|$ is 3.

(b) $|-6| + 9$

1. Begin by evaluating the absolute value of $-6$: $|-6| = 6$
2. Now, add 9 to the result: $6 + 9 = 15$

So, the result of $|-6| + 9$ is 15.

If you'd like more detailed explanations or have any questions, feel free to ask!

Here are 5 related questions you might consider:

1. What is the absolute value of $-10$?
2. How does the order of operations affect solving absolute value equations?
3. What is the result of $|4 - 8|$?
4. Can absolute value ever be negative?
5. How would you solve an equation involving multiple absolute values, such as $|x| + |y|$?

Tip: Always simplify the expression inside the absolute value first before applying the absolute value function.