Final answer:
The perimeter of the rectangle with the given length and width expressions is calculated using the formula P = 2(length + width), resulting in a perimeter expression of 4x - 18y - 4.
Step-by-step explanation:
The student is asking for the perimeter of a rectangle with given length and width expressions. The formula for the perimeter of a rectangle is P = 2(length + width). Plugging in the expressions for length (4x - 5y - 8) and width (-2x - 4y + 6), we get:
P = 2[(4x - 5y - 8) + (-2x - 4y + 6)]
Simplifying within the brackets first:
P = 2[(4x - 2x) - (5y + 4y) - (8 - 6)]
P = 2[(2x) - (9y) - (2)]
Then we apply the distributive property:
P = 2(2x) - 2(9y) - 2(2)
P = 4x - 18y - 4
Therefore, the correct answer is 4x - 18y - 4, which is not listed among the provided options, indicating a potential issue with the question or answer choices.