Question

Four types of energy?

Answer 1

Potential Energy is any type of stored energy. It can be chemical, nuclear, gravitational, or mechanical.Kinetic  ...GRAVITATIONAL.CHEMICAL.NUCLEAR.
even motion.

Answer 2

The types of energy are:
Kinetic: When an object has energy through movement.
Thermal: When an object has energy from heat
Gravitational: When an object has energy from height above a surface
Elastic: when an object has energy from being stretched or squashed
Chemical: When an object has energy from chemical reactions
There is also nuclear energy but that probably isn't what you need

Hope this helps :)