Answer:

System Description:
- The system consists of two energy levels, one at -2E and the other at 2E.
- The lower energy level is 3-fold degenerate, meaning there are three distinct states with the same energy (-2E).
- The upper energy level is non-degenerate, implying that there is only one state at that energy (2E).
- The system is in thermodynamic equilibrium at temperature T.
- There are N classical non-interacting particles in the system.

Explanation:

1. Energy Levels and Degeneracy:
- The lower energy level (-2E) is 3-fold degenerate, meaning there are three distinct states with the same energy.
- The upper energy level (2E) is non-degenerate, indicating that there is only one state at that energy.

2. Thermodynamic Equilibrium:
- The system is in thermodynamic equilibrium, implying that the macroscopic properties of the system do not change with time.
- At equilibrium, the distribution of particles among different energy levels follows the Boltzmann distribution.
- The probability of finding a particle in a particular energy state is given by the Boltzmann factor: P(E) = exp(-E/kT), where E is the energy of the state, k is the Boltzmann constant, and T is the temperature.
- In this case, the lower energy level (-2E) will have a higher probability of being occupied compared to the upper energy level (2E) due to the negative sign in the exponent.

3. Number of Particles:
- There are N classical non-interacting particles in the system.
- The distribution of particles among energy levels follows the principle of equipartition of energy, which states that each degree of freedom contributes 1/2 kT to the total energy on average.
- Since the lower energy level is 3-fold degenerate, each state contributes 1/2 kT to the total energy, resulting in a total contribution of 3/2 kT.
- The upper energy level is non-degenerate, contributing only 1/2 kT to the total energy.
- Therefore, the total energy of the system is (3/2 + 1/2) kT = 2kT.

4. Correct Statements:
Based on the given information, the following statements are correct:

- The lower energy level is 3-fold degenerate.
- The upper energy level is non-degenerate.
- The distribution of particles among energy levels follows the Boltzmann distribution.
- The lower energy level is more likely to be occupied compared to the upper energy level due to the negative sign in the exponent.
- The total energy of the system is 2kT.

Conclusion:
Based on the given information, we can conclude that the correct statements are the ones mentioned above.