Let's evaluate the expressions given in the image step by step:

(a) $|-4| + 9$

1. The absolute value of $-4$ is 4, because absolute values turn negative numbers positive.
2. Now, add $4 + 9 = 13$.

Thus, the result of (a) is 13.

(b) $-4 + |9|$

1. The absolute value of $9$ is 9, as positive numbers remain the same under absolute value.
2. Now, add $-4 + 9 = 5$.

Thus, the result of (b) is 5.

Would you like more details on any of the steps? Here are some related questions to expand on this:

1. What are the properties of absolute values?
2. How do absolute values affect negative numbers?
3. How can you simplify expressions involving absolute values?
4. What is the difference between absolute value and regular addition?
5. Can you explain how to solve similar problems with larger numbers?

Tip: Remember that absolute value only affects the sign of numbers, making them non-negative.