A) \( 4: 2 \cdot 3-4^{2}+9: 3 \)

Let’s break it down step by step to get this evaluation done: 1. Start with the expression: \( 4: 2 \cdot 3 - 4^{2} + 9: 3 \). 2. According to the order of operations, we evaluate any parentheses or exponents first. Here, we have \( 4^{2} = 16 \). 3. Now, rewrite the expression: \( 4: 2 \cdot 3 - 16 + 9: 3 \). 4. Next, perform the division: \( 4: 2 = 2 \) and \( 9: 3 = 3 \). 5. Now the expression simplifies to: \( 2 \cdot 3 - 16 + 3 \). 6. Next, perform the multiplication: \( 2 \cdot 3 = 6 \). 7. The expression now looks like: \( 6 - 16 + 3 \). 8. Perform the subtraction: \( 6 - 16 = -10 \). 9. Finally, add: \( -10 + 3 = -7 \). So, the final result of evaluating the expression \( 4: 2 \cdot 3 - 4^{2} + 9: 3 \) is \( -7 \).