Elastic potential energy is the energy stored in an elastic object when it is either compressed or stretched. This type of energy is a result of the object's ability to return to its original shape after being deformed. Elastic potential energy can be achieved by compressing or stretching the body, which is why the correct answer is option 'D'.

Here's a detailed explanation of why compressing or stretching the body can result in elastic potential energy:

1. Definition of elastic potential energy:
- Elastic potential energy is a form of potential energy stored in elastic materials, such as springs or rubber bands.
- It arises from the deformation of the material, and the energy is stored when the material is compressed or stretched.

2. How compression leads to elastic potential energy:
- When a body is compressed, its particles are pushed closer together, causing the object to deform and store potential energy.
- For example, consider a spring. When a force is applied to compress the spring, it resists the compression and stores potential energy.
- The potential energy is directly proportional to the amount of compression. The more the spring is compressed, the more potential energy it stores.

3. How stretching leads to elastic potential energy:
- When a body is stretched, its particles are pulled farther apart, causing the object to deform and store potential energy.
- For instance, imagine a rubber band. When it is stretched, it resists the stretching and stores potential energy.
- The potential energy is directly proportional to the amount of stretch. The more the rubber band is stretched, the more potential energy it stores.

4. Elastic potential energy and Hooke's Law:
- Hooke's Law states that the force needed to compress or stretch an elastic object is directly proportional to the amount of deformation.
- Mathematically, this can be expressed as F = kx, where F is the force applied, k is the spring constant, and x is the displacement from the equilibrium position.
- The potential energy stored in the object is given by the equation PE = (1/2)kx^2, where PE is the elastic potential energy.
- This equation shows that the potential energy is directly proportional to the square of the displacement.

In conclusion, compressing or stretching a body allows it to store elastic potential energy. This energy is stored in the object's deformed state and can be released when the object returns to its original shape.