To find the perimeter of a rectangle with a width of $8u - 4$ cm and a length of $8u - 2$ cm, we use the formula for the perimeter of a rectangle:

$P = 2 \times (\text{length} + \text{width})$

Step-by-Step Solution

1. Substitute the given values: $P = 2 \times ((8u - 4) + (8u - 2))$

2. Combine like terms inside the parentheses: $P = 2 \times (8u + 8u - 4 - 2)$ Simplify this to: $P = 2 \times (16u - 6)$

3. Distribute the 2: $P = 2 \times 16u - 2 \times 6$ $P = 32u - 12$

So, the correct expression representing the perimeter is:

$\boxed{-12 + 32u}$

Answer: The correct option is $-12 + 32u$.

Would you like further details or have questions on this?

Here are some related questions to consider:

1. How would the formula change if only the width was given, not the length?
2. What if the units of the rectangle were in meters instead of centimeters?
3. How would you calculate the area with the same length and width?
4. What if the rectangle was actually a square with $8u - 4$ as both length and width?
5. How do you determine if an expression is equivalent to a perimeter formula?

Tip: When calculating perimeter or area, always ensure like terms are combined properly for accuracy.