We are given the expression:

$-1 \cdot (4) \cdot (-2) \cdot (-2)$

To evaluate this, we will multiply the numbers step by step.

Step 1: Multiply the first two numbers

$-1 \cdot 4 = -4$

Step 2: Multiply the result by the next number

$-4 \cdot (-2) = 8$

Step 3: Multiply the result by the last number

$8 \cdot (-2) = -16$

Final Result:

$-1 \cdot 4 \cdot (-2) \cdot (-2) = -16$

The evaluated result is -16.

Would you like any further details or explanations? Here are some related questions you might find helpful:

1. How do the rules for multiplying negative numbers work?
2. What is the difference between multiplying an even and an odd number of negative numbers?
3. How do the associative and commutative properties of multiplication affect solving such problems?
4. How does this problem relate to solving equations in algebra?
5. What would change if we used division instead of multiplication?

Tip: When multiplying several numbers, especially with negative signs, always count the number of negative numbers. An even number of negatives will result in a positive product, while an odd number of negatives will result in a negative product.