A spring with spring constant k has two equal masses attached to...

Let the total extension of the spring be $x$.

The total work done by the spring on both masses is equal to the negative of the potential energy stored in the spring:

$W_{total} = -\dfrac{1}{2}kx^2$

Since the two masses are equal and are pulled symmetrically, the displacement of each mass is equal and opposite. The work done by the spring on each mass is identical.

Let $W$ be the work done by the spring on each mass. Then:

$2W = W_{total} = -\dfrac{1}{2}kx^2$

$W = -\dfrac{1}{4}kx^2$

Alternatively, when the spring is stretched by a distance $y$, the restoring force on each mass is $ky$ directed inwards. The displacement of each mass is $dy/2$ outwards.

The work done by the spring on one mass is:

$W = \int_{0}^{x} (-ky) d\left(\dfrac{y}{2}\right) = -\dfrac{k}{2} \int_{0}^{x} y \, dy = -\dfrac{1}{4}kx^2$