Let's break down the expression:

\[
-3x^{-2}(-4x^4)
\]

### Step-by-step solution:

1. **Multiply the constants**:  
   \(-3\) and \(-4\) multiply to give:
   \[
   (-3)(-4) = 12
   \]

2. **Multiply the powers of \(x\)**:  
   When multiplying powers of the same base, we add the exponents. In this case, the exponents are \(-2\) and \(4\):
   \[
   x^{-2} \cdot x^4 = x^{-2 + 4} = x^2
   \]

3. **Final expression**:  
   Combining the results, we get:
   \[
   12x^2
   \]

### Final Answer:
\[
12x^2
\]

Would you like more details on any part of the process?

Here are five related questions to expand your understanding:
1. How do you simplify expressions with negative exponents?
2. What is the rule for multiplying powers of the same base?
3. Can you explain how to deal with expressions involving both negative and fractional exponents?
4. How would you simplify \((-2x^{-3})(5x^5)\)?
5. What are the rules for distributing exponents in more complex expressions?

**Tip**: Always remember the basic exponent rule: when multiplying like bases, you add the exponents.

This detailed solution simplifies the expression -3x^-2(-4x^4) using exponent multiplication rules and negative exponents. It covers algebraic concepts, including multiplying constants and powers. Suitable for students in Grades 9-10.

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