To solve this, we need to simplify $2 \sqrt{-32}$.

Step-by-Step Solution:

1. Handle the Negative Inside the Square Root: $\sqrt{-32} = \sqrt{-1 \cdot 32} = \sqrt{-1} \cdot \sqrt{32}$ Since $\sqrt{-1} = i$ (where $i$ is the imaginary unit), we get: $\sqrt{-32} = i \cdot \sqrt{32}$

2. Simplify $\sqrt{32}$: Break down 32 into factors: $\sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2}$ Thus, $\sqrt{-32} = i \cdot 4\sqrt{2} = 4i\sqrt{2}$

3. Multiply by 2: Now we go back to the original expression, $2 \cdot \sqrt{-32}$: $2 \cdot \sqrt{-32} = 2 \cdot (4i\sqrt{2}) = 8i\sqrt{2}$

Conclusion:

The correct answer is: $\boxed{8i\sqrt{2}}$

Would you like more details, or do you have any questions about the solution?

Here are some related questions to practice:

1. What is $\sqrt{-64}$ simplified?
2. How would you simplify $3 \sqrt{-18}$?
3. What is the value of $\sqrt{-50}$ in terms of $i$?
4. If $\sqrt{-72}$ is simplified, what would the result be?
5. What is the simplified form of $5 \sqrt{-8}$?

Tip: Remember that $i$ represents $\sqrt{-1}$, and this is essential when dealing with square roots of negative numbers.