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?

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!