In mathematics, the order of operations is commonly remembered as PEMDAS or BODMAS. Parentheses or brackets come first, followed by exponents or orders. Next, multiplication and division are completed according to their equal priority, working from left to right when necessary. Addition and subtraction follow afterward.

Our equation contains addition, division, and multiplication: 8 + 8 ÷ 8 + 8 × 0. Before performing any addition, we must calculate the division and multiplication. First, look at 8 ÷ 8. Any nonzero number divided by itself equals 1, so 8 ÷ 8 = 1.

Next, look at the multiplication: 8 × 0. Any number multiplied by zero equals 0, so 8 × 0 = 0. Now we can replace those parts of the original expression with their calculated values. The equation becomes 8 + 1 + 0.

Now only addition remains. Working from left to right, 8 + 1 = 9, and then 9 + 0 = 9. Therefore, the mathematically correct answer is 9. The puzzle becomes straightforward once the standard order of operations is followed. The important lesson is not to rush through an expression simply from left to right. Complete multiplication and division before addition and subtraction, and puzzles like this become much easier to solve correctly.