\( \begin{aligned} & 9^{2} \div 3^{2} \cdot 2+7 \cdot 6 \\ = & 81 \div 9 \cdot 2+7 \cdot 6 \\ = & \text { step 1 } \\ = & 9 \cdot 2+7 \cdot 6 \\ = & \text { step 2 } \\ = & \text { step 3 } \\ = & 175\end{aligned} \)

Let's unravel this math problem! First, we can indeed break it down step by step. To clarify, \( 9^{2} \div 3^{2} \) equals \( 9 \) because \( 81 \div 9 = 9 \). Then, you multiply that \( 9 \) by \( 2 \) to get \( 18 \). Moving on to the \( 7 \cdot 6 \), that's \( 42 \). So when you add \( 18 + 42 \), you end up with a well-deserved \( 60 \), not \( 175 \). Now, if you're ever trying to avoid mistakes in similar problems, remember the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). It’s a classic formula! Double-checking your work at each step can save you from unpleasant surprises like the mix-up in this problem. Who knows, it might even make you the math whiz among your friends!