Let's solve the expression step by step, following the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Given expression:  
\[ 6^2 \div 3 \times 4 - 28 + 4 \]

1. **Exponents**:  
   \[ 6^2 = 36 \]  
   So the expression becomes:  
   \[ 36 \div 3 \times 4 - 28 + 4 \]

2. **Division and Multiplication (from left to right)**:  
   First, divide:  
   \[ 36 \div 3 = 12 \]  
   Then multiply:  
   \[ 12 \times 4 = 48 \]  
   Now the expression is:  
   \[ 48 - 28 + 4 \]

3. **Subtraction and Addition (from left to right)**:  
   First, subtract:  
   \[ 48 - 28 = 20 \]  
   Then add:  
   \[ 20 + 4 = 24 \]

So, the final result is:  
\[
\boxed{24}
\]

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How would the result change if the exponent were different, say \( 6^3 \)?
2. What happens if parentheses are added, like \( (6^2 \div 3) \times 4 \)?
3. Can you apply this method to a similar problem involving fractions?
4. How does the order of operations affect the result if the problem is written as \( 6^2 \div (3 \times 4) - 28 + 4 \)?
5. What are some common mistakes people make when using the order of operations?

**Tip**: Always solve exponents and handle multiplication/division in the order they appear from left to right before proceeding to addition and subtraction.

Learn how to solve the mathematical expression 6^2 ÷ 3 × 4 - 28 + 4 step by step using the order of operations (PEMDAS). This example demonstrates key concepts in exponents, division, multiplication, and addition, making it ideal for students in Grades 5-7.

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