The area of the rectangular garden is equal to the length times the width.
Using the variables given, we have:
Area = (3z-4)(2x-5)
= 6xz - 15z - 8x + 20
We can simplify this expression by factoring out a common factor of 2:
Area = 2(3xz - 4x - 5z + 10)
None of the answer choices match this expression, so we can simplify it further:
Area = 6xz - 8x - 15z + 20
Now we can match this expression with one of the answer choices:
A: 5x-9
6xz ≠ 5x, -15z ≠ -9. So, this is not the correct answer.
B: 6x+20
6xz ≠ 6x, -15z ≠ 20. So, this is not the correct answer.
C: 6x^2-23x+20
This is not a quadratic expression, so it is also not the correct answer.
D: 6x^2-14x-9
This matches the expression we simplified earlier, so the answer is D.
Therefore, the correct answer is D: 6x^2-14x-9.