The perimeter $P$ of a rectangle is calculated by adding up the lengths of all its sides. For a rectangle, the formula is:

$P = 2 \times (\text{Length} + \text{Width})$

In the image, the length of the rectangle is given as $3x - 2$, and the width is $2x - 8$.

So, the expression for the perimeter is:

$P = 2 \times \left( (3x - 2) + (2x - 8) \right)$

Now, simplify the expression inside the parentheses:

$(3x - 2) + (2x - 8) = 3x + 2x - 2 - 8 = 5x - 10$

Substitute this back into the formula for the perimeter:

$P = 2 \times (5x - 10) = 10x - 20$

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

$P = 10x - 20$

Would you like more details or have any questions? Here are 5 related questions to consider:

1. How do we find the perimeter of more complex polygons?
2. Can you express the perimeter as a function of $x$?
3. What is the perimeter if $x = 5$?
4. How does the perimeter change as $x$ increases?
5. How would you solve for $x$ if the perimeter were given?

Tip: When working with expressions in geometry, always remember to group like terms to simplify calculations.