Option D: Y, V and W are parallel.
     ● Statement 1: Line X is perpendicular to line Y and parallel to line Z.  
           ○ This implies that line X and line Z are both perpendicular to line Y.
     ● Statement 2: Line U is perpendicular to both lines V and W.  
           ○ This implies that lines V and W are parallel to each other because they share a common perpendicular line, U.
     ● Statement 3: Line X is perpendicular to line V.  
           ○ Since line X is perpendicular to line V, and line X is also perpendicular to line Y (from Statement 1), lines V and Y must be parallel to each other because they share a common perpendicular line, X.
     ● Conclusion:  
           ○ From Statement 2, we know that lines V and W are parallel.
           ○ From Statement 3, we know that lines V and Y are parallel.
           ○ Therefore, lines Y, V, and W are all parallel to each other.
     ● Verification of Options:  
       ● Option A: Z, U, and W are parallel. This is incorrect because U is perpendicular to W.  
       ● Option B: X, V, and Y are parallel. This is incorrect because X is perpendicular to both V and Y.  
       ● Option C: Z, V, and U are all perpendicular to W. This is incorrect because V is parallel to W.  
       ● Option D: Y, V, and W are parallel. This is correct as explained above.  
     ● Final Answer: The correct statement is Option D: Y, V, and W are parallel.