https://file.aiquickdraw.com/mathbot/file/1728036746756nbwpqt2g.jpg

The expression to evaluate is:

\[
|2| + |-12| - |2| + |-101| - |-101|
\]

### Step-by-step solution:

1. **Absolute Values:**
   - \(|2| = 2\)
   - \(|-12| = 12\)
   - \(|2| = 2\)
   - \(|-101| = 101\)

So, the expression becomes:

\[
2 + 12 - 2 + 101 - 101
\]

2. **Simplify the Expression:**
   - \(2 - 2 = 0\)
   - \(12 + 101 - 101 = 12\)

Thus, the final result is:
\[
\boxed{12}
\]

The correct answer is option (b) \(12\).

Would you like more details or have any other questions?

Here are 5 related questions for further exploration:
1. What are absolute values and how do they affect negative numbers?
2. How does the order of operations apply in this expression?
3. Can absolute values ever be negative?
4. What would happen if we changed all the positive numbers in the expression to negative?
5. How do absolute values behave when dealing with complex numbers?

**Tip:** Always resolve absolute values first in an expression to simplify calculations.

This problem demonstrates how to evaluate an arithmetic expression involving absolute values: |2| + |-12| - |2| + |-101| - |-101|. Learn the step-by-step approach to simplify such expressions, focusing on the properties of absolute values and basic arithmetic operations. Ideal for Grades 6-8 students.

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