The internal energy (U) of a gas depends on its degrees of freedom (f).

For a monatomic gas like neon, the degrees of freedom are f = 3 (translational). For a diatomic gas like oxygen, the degrees of freedom are f = 5 (3 translational + 2 rotational).

The internal energy for each component of the gas mixture can be calculated using the formula:

$$U = \frac{f}{2}nRT$$

where n is the number of moles, R is the universal gas constant, and T is the temperature.

For the 4 moles of neon (monatomic):

$$U_{Ne} = \frac{3}{2} \cdot 4RT = 6RT$$

For the 2 moles of oxygen (diatomic):

$$U_{O_2} = \frac{5}{2} \cdot 2RT = 5RT$$

Now, to find the total internal energy, we sum the internal energies of the individual components:

$$U_{total} = U_{Ne} + U_{O_2} = 6RT + 5RT = 11RT$$

Thus, the total internal energy of the system is 11RT.