1. The problem is to simplify the expression $(2\sqrt{2})^2$. 2. First, recognize that $(a b)^2 = a^2 b^2$ for any real numbers $a$ and $b$. 3. Apply this property to get $(2\sqrt{2})^2 = 2^2 \times (\sqrt{2})^2$. 4. Calculate each part: $2^2 = 4$ and $(\sqrt{2})^2 = 2$. 5. Multiply these results: $4 \times 2 = 8$. 6. Therefore, the expression $(2\sqrt{2})^2$ simplifies to $8$. 7. The final answer is $8$.