The expression to simplify is:

$\sqrt{-4} \cdot \sqrt{-36}$

Since both of these square roots involve negative numbers, we need to express them in terms of the imaginary unit $i$, where $i = \sqrt{-1}$.

1. First, simplify each square root separately: $\sqrt{-4} = \sqrt{4} \cdot \sqrt{-1} = 2i$ $\sqrt{-36} = \sqrt{36} \cdot \sqrt{-1} = 6i$

2. Now, multiply the results: $2i \cdot 6i = 12i^2$

3. Recall that $i^2 = -1$, so: $12i^2 = 12 \cdot (-1) = -12$

Therefore, the simplified answer is: $\boxed{-12}$

Would you like further details or explanations?

Here are five related questions:

1. What is the imaginary unit $i$ and why is $i^2 = -1$?
2. How do you handle square roots of negative numbers in general?
3. Can complex numbers be represented geometrically?
4. How do we multiply two complex numbers?
5. What is the general form of a complex number?

Tip: When working with square roots of negative numbers, always remember to factor out $\sqrt{-1}$ as $i$ before simplifying.