A gas mixture consists of 2 moles of oxygen and 4 moles of neon at...

The internal energy of a gas is given by $U = n{C}_{V}T$.

A diatomic gas has $3$ translational and $2$ rotational degrees of freedom. A monoatomic gas has $3$ translational degrees of freedom.

Hence, the internal energy of the mixture $= {n}_{1}{C}_{{V}_{1}}T + {n}_{2}{C}_{{V}_{2}}T$

$= 2 \times \left(\dfrac{5R}{2}\right)T + 4 \times \dfrac{3R}{2}T = 5RT + 6RT$

$= 11RT$