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Let's go through each part:

### Problem (a)
1. **Calculate** \( |8 - 12| \):
   - \( 8 - 12 = -4 \)
   - \( |-4| = 4 \)
   - So, \( |8 - 12| = 4 \).

2. **Calculate** \( |8| - |12| \):
   - \( |8| = 8 \) and \( |12| = 12 \)
   - So, \( |8| - |12| = 8 - 12 = -4 \).

3. **Compare** \( |8 - 12| \) and \( |8| - |12| \):
   - \( |8 - 12| = 4 \) and \( |8| - |12| = -4 \)
   - Since \( 4 \neq -4 \), the answer is **No (N)**.

### Problem (b)
1. **Calculate** \( |12 - 8| \):
   - \( 12 - 8 = 4 \)
   - \( |4| = 4 \)
   - So, \( |12 - 8| = 4 \).

2. **Calculate** \( |12| - |8| \):
   - \( |12| = 12 \) and \( |8| = 8 \)
   - So, \( |12| - |8| = 12 - 8 = 4 \).

3. **Compare** \( |12 - 8| \) and \( |12| - |8| \):
   - \( |12 - 8| = 4 \) and \( |12| - |8| = 4 \)
   - Since \( 4 = 4 \), the answer is **Yes (Y)**.

### Summary of Answers
- **(a)** \( |8 - 12| = 4 \), \( |8| - |12| = -4 \), answer: **No (N)**
- **(b)** \( |12 - 8| = 4 \), \( |12| - |8| = 4 \), answer: **Yes (Y)**

Would you like more detailed explanations or have any questions?

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Here are 5 related questions to deepen your understanding:
1. Why does the absolute value make negative results positive?
2. How would these calculations change if we used addition instead of subtraction?
3. What properties of absolute values can be observed here?
4. Can we conclude a general rule for \( |a - b| \) vs. \( |a| - |b| \) based on this?
5. How would the results change if \( a \) and \( b \) were negative?

**Tip:** When comparing expressions, compute each part separately to avoid sign errors!

Construct viable arguments.
Enter the correct answers in the boxes.
Enter 'Y' for Yes and 'N' for No

a. |8 - 12| = __, |8| - |12| = __. Is |8 - 12| = |8| - |12|? (Y/N)

b. |12 - 8| = __, |12| - |8| = __. Is |12 - 8| = |12| - |8|? (Y/N)

Learn how to solve absolute value expressions such as |8 - 12| and |12 - 8| with step-by-step calculations. This example demonstrates the properties of absolute values and inequalities, ideal for students in Grades 6-8.

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