Let's solve the expression \([4(12 - 6) / 2]^2\) step by step.

1. **Solve inside the parentheses**:  
   \( 12 - 6 = 6 \)

   Now the expression becomes:
   \[
   [4(6) / 2]^2
   \]

2. **Multiply**:  
   \( 4 \times 6 = 24 \)

   Now the expression becomes:
   \[
   [24 / 2]^2
   \]

3. **Division**:  
   \( 24 / 2 = 12 \)

   Now the expression becomes:
   \[
   12^2
   \]

4. **Square the result**:  
   \( 12^2 = 144 \)

Thus, the final answer is:
\[
\boxed{144}
\]

Would you like more details or have any questions?

Here are some related questions to further explore:
1. How do you handle expressions with multiple sets of parentheses?
2. What is the difference between squaring a number and taking the square root?
3. How does the order of operations affect the result in complex expressions?
4. What are some common mistakes made when simplifying algebraic expressions?
5. Can you show how to simplify similar expressions with fractions?

**Tip**: Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) to avoid mistakes in complex calculations!

Learn how to solve the arithmetic expression [4(12-6)/2]^2 by following the order of operations (PEMDAS). This step-by-step solution covers key concepts such as parentheses, exponents, and basic arithmetic, making it ideal for students in Grades 6-8.

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