Key Concepts:
- The work done to change the distance between the plates of a parallel plate capacitor is equal to the change in potential energy of the system.
- The potential energy stored in a capacitor is given by U = (1/2)CV^2, where C is the capacitance and V is the potential difference between the plates.
- Doubling the distance between the plates of a capacitor will result in a halving of the capacitance.

Solution:
To find the work required to double the distance between the plates of a parallel plate capacitor, we need to consider the change in potential energy of the system.

Step 1: Determine the initial potential energy of the capacitor.
The initial potential energy (U1) of the capacitor is given by U1 = (1/2)CV^2, where C is the capacitance and V is the potential difference between the plates.

Step 2: Determine the final potential energy of the capacitor.
To double the distance between the plates, the capacitance (C) of the capacitor will be halved. Therefore, the final potential energy (U2) of the capacitor is given by U2 = (1/2)(C/2)V^2.

Step 3: Calculate the work done.
The work done (W) to change the distance between the plates is equal to the change in potential energy, which is given by W = U2 - U1.

Step 4: Substitute the values and simplify.
W = U2 - U1
W = (1/2)(C/2)V^2 - (1/2)CV^2
W = (1/4)CV^2 - (1/2)CV^2
W = -(1/4)CV^2

Conclusion:
The work required to double the distance between the plates of a parallel plate capacitor is -(1/4)CV^2. Therefore, the correct option is (3) 1/8CV^2.