This is the match:
1) stored energy related to positions of atoms within molecules ↔ chemical energy
Explanation: the chemical energy is the energy stored in the bonds that binds the atoms that form the molecules.
2) energy released when a nucleus splits or combines ↔ nuclear energy
Explanation: there is a huge energy inside an atom which may be released when nuclei suffer fusion (combination of nuclei) or fission (split of nuclei). The fusion of atoms is what happens in stars and it is the source of their energy. Fision of atoms is the nuclear energy used in the nuclear plants to produce electricity.
3) energy related to an object's movement ↔ motion energy
Step-by-step explanation:
The motion energy is the kinetic energy, KE. KE = (1/2) m* v^2
4) energy related to heigth ↔ gravitaional potential energy
The higher an object is the higher its gravitational potential energy, PE.
PE = m*g*h.
5) energy related by vibration of a string ↔ sound energy
Step-by-step explanation:
Sure you have seen that: when the string of a guitar vibrate the sound is produced.
6) energy of motion of particles in a substance ↔ thermal energy
The thermal energy is the product of the motions (vibration, translation and collisions) of the molecules that form the substance. The higher the motion the the higher the thermal energy measured as temperature.