The expression provided in the image is:

$6 + 4 \cdot 3 + 12 \div 2$

To solve it, we must follow the order of operations, which is often remembered by the acronym PEMDAS:

• Parentheses first,
• Exponents (powers and roots),
• MD Multiplication and Division (from left to right),
• AS Addition and Subtraction (from left to right).

Let's apply this step by step:

1. First, handle the multiplication and division: $4 \cdot 3 = 12 \quad \text{and} \quad 12 \div 2 = 6$

   So the expression becomes: $6 + 12 + 6$

2. Now, perform the addition: $6 + 12 + 6 = 24$

Thus, the final result is 24.

The correct answer is 24.

Would you like more details or have any questions? Here are 5 related questions for further learning:

1. How would the answer change if parentheses were added around $4 \cdot 3 + 12$?
2. What is the difference between the order of operations in PEMDAS and BODMAS?
3. How does the order of operations affect calculations in longer algebraic expressions?
4. If the division in the expression were a fraction, how would that affect the solution?
5. How does distributing multiplication over addition differ from following PEMDAS?

Tip: Always handle multiplication and division from left to right before moving on to addition and subtraction.