To simplify the expression $-2i \cdot (-3i)$, let's proceed with the following steps:

1. Multiply the constants: $-2 \times -3 = 6$.
2. Multiply the imaginary units: $i \times i = i^2$.

Since $i^2 = -1$, we get: $6 \cdot i^2 = 6 \cdot (-1) = -6$

Therefore, the simplified answer is $-6$.

Would you like more details or have any questions?

Here are some related questions to explore further:

1. What happens when we multiply two imaginary numbers with different signs?
2. How is $i^2 = -1$ derived, and what does it represent in complex numbers?
3. What would the result be if both imaginary numbers had positive signs?
4. How would the answer change if we had a real number multiplied by an imaginary number?
5. What is the effect of squaring an imaginary number?

Tip: Remember, $i^2 = -1$ is a fundamental property of imaginary numbers, and it helps simplify expressions involving powers of $i$.