The expression shown in the image is:

$\sqrt{-4} \cdot \sqrt{-12}$

To solve this, we recognize that both square roots involve negative numbers, which introduces imaginary numbers. The square root of a negative number can be written as a multiple of $i$, where $i = \sqrt{-1}$.

Step-by-step solution:

1. Express the square roots of negative numbers using $i$: $\sqrt{-4} = \sqrt{4} \cdot i = 2i$ $\sqrt{-12} = \sqrt{12} \cdot i = \sqrt{4 \times 3} \cdot i = 2\sqrt{3} \cdot i$

2. Now multiply the two terms: $\sqrt{-4} \cdot \sqrt{-12} = (2i) \cdot (2\sqrt{3}i)$

3. Multiply the constants and $i$ terms: $(2 \cdot 2\sqrt{3}) \cdot (i \cdot i) = 4\sqrt{3} \cdot (-1) = -4\sqrt{3}$

So, the result of the expression is: $-4\sqrt{3}$

Would you like more details or further clarifications on any step?

Here are some related questions for further practice:

1. How do you simplify expressions involving imaginary numbers?
2. What is the square root of a negative number in terms of $i$?
3. Can you explain why $i^2 = -1$?
4. How would you multiply two complex numbers?
5. What is the general form of a complex number?

Tip: Whenever you deal with square roots of negative numbers, always introduce the imaginary unit $i$ before performing other operations.