Let's simplify the expression:
$3 \sqrt{-16} + 6 \sqrt{-4}$

1. Simplifying $\sqrt{-16}$ and $\sqrt{-4}$:
   We know that the square root of a negative number involves i, the imaginary unit, where $i = \sqrt{-1}$.

   • $\sqrt{-16} = \sqrt{16} \times \sqrt{-1} = 4i$
   • $\sqrt{-4} = \sqrt{4} \times \sqrt{-1} = 2i$

2. Now, substitute these back into the expression: $3(4i) + 6(2i) = 12i + 12i$

3. Combine like terms: $12i + 12i = 24i$

Thus, the simplified result is: $24i$

Would you like further details on imaginary numbers or square roots of negative numbers? Here's a list of related questions:

1. What is the imaginary unit $i$ and how is it used?
2. Can you explain the difference between real and imaginary numbers?
3. How do you simplify expressions involving $\sqrt{-1}$?
4. What are complex numbers and how do they relate to imaginary numbers?
5. How do you add and subtract imaginary numbers?

Tip: Imaginary numbers help represent quantities that cannot be expressed as real numbers, such as the square root of negative numbers.