To find the perimeter of a rectangle, you can use the formula:

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

Given the width $(8u - 4)$ cm and the length $(8u - 2)$ cm, we can substitute these expressions into the formula.

First, add the length and the width:

$\text{length} + \text{width} = (8u - 2) + (8u - 4)$

Combine like terms:

$(8u - 2) + (8u - 4) = 8u + 8u - 2 - 4 = 16u - 6$

Now, multiply this sum by 2 to find the perimeter:

$P = 2 \times (16u - 6)$

Distribute the 2:

$P = 2 \times 16u - 2 \times 6 = 32u - 12$

Thus, the expression that represents the perimeter of the rectangle is:

$\boxed{32u - 12 \text{ cm}}$

Would you like more details or have any questions about this solution?

Here are 5 related questions to expand your understanding:

1. How do you find the area of a rectangle given its length and width?
2. What happens to the perimeter of a rectangle if both the length and the width are doubled?
3. How do you express the perimeter of a square in terms of the side length?
4. If $u = 1$, what is the perimeter of this rectangle?
5. How would you find the length and width if the perimeter and one dimension were given?

Tip: When combining like terms, make sure to align similar variables to simplify the expression accurately.