To solve the expression $8÷2(4-2)$, we need to follow the order of operations, often remembered by the acronym PEMDAS or BODMAS (Parentheses or Brackets, Exponents or Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Let’s break it down step by step:

1. Parentheses: First, solve the operation inside the parentheses: $4-2=2$ Now, the expression simplifies to: $8÷2(2)$
2. Implied Multiplication: Here, $2(2)$ means $2\times 2$: $8÷2\times 2$
3. Multiplication and Division (Left to Right): According to the order of operations, we process multiplication and division as they appear from left to right:
   • First, divide 8 by 2: $8÷2=4$
   • Then, multiply the result by 2: $4\times 2=8$

So, the final answer is: $8$

Common Misunderstandings

The confusion often arises because of the way the problem is written. Some might misinterpret it as: $8÷(2\times 2)$ However, without additional parentheses to change the order, we strictly follow left-to-right processing for multiplication and division, leading to the answer 8.

Visualizing the Steps

To ensure clarity:

1. Solve within parentheses: $4-2=2$
2. Reinterpret the expression: $8÷2\times 2$
3. Process division and multiplication from left to right: $8÷2=4$ $4\times 2=8$

Thus, the correct interpretation using standard mathematical rules results in $8$.