Both ends of a spring are displaced along its length. Every...

Let the magnitude of displacement of each end be $x$.

The tension or compression in a spring is proportional to the change in its length.

When the right end is shifted leftward and the left end rightward, the spring is compressed by $2x$. The magnitude of deformation is $2x$.

When both ends are shifted in the same direction (both leftward or both rightward), the net change in the length of the spring is zero.

When the right end is shifted rightward and the left end leftward, the spring is elongated by $2x$. The magnitude of deformation is $2x$.

Since the maximum change in length is $2x$, the tension or compression attains a maximum magnitude in the first and fourth cases.