The problem asks to simplify the expression $(-3 - 6i) - (3 - 6i)$.

Let's break it down step by step:

1. Distribute the negative sign across the second set of parentheses: $(-3 - 6i) - (3 - 6i) = -3 - 6i - 3 + 6i$

2. Combine the real parts and the imaginary parts:

   • The real parts: $-3 - 3 = -6$
   • The imaginary parts: $-6i + 6i = 0$

So, the simplified expression is: $-6$

The correct answer is: $-6$.

Would you like any further details or explanations?

Here are 5 related questions to consider:

1. What are the rules for adding and subtracting complex numbers?
2. How would the result change if one of the imaginary parts were different?
3. What happens when you multiply complex numbers instead of subtracting them?
4. How can you express the result in polar form?
5. What are the applications of complex numbers in electrical engineering?

Tip: When subtracting complex numbers, make sure to treat real and imaginary parts separately.