Let's simplify the expression step by step:
We start with: \[ (2u - 7y) - (7u + 2y) \]
First, distribute the negative sign across the second term: \[ = 2u - 7y - 7u - 2y \]
Now, combine like terms:
For the \(u\) terms: \[ 2u - 7u = -5u \]
For the \(y\) terms: \[ -7y - 2y = -9y \]
Combining both results, we have: \[ -5u - 9y \]
The result matches option D. Thus, the answer is: \[ \boxed{-5u - 9y} \]