The length of the edge of the base of a right square prism is 6 units.

Choice D is correct. The volume, $V$, of a right square prism is given by the formula $V=s^{2}h$, where $s$ represents the length of the edge of the base and $h$ represents the height of the prism. It’s given that the volume of a right square prism is $\mathrm{2,880}$ cubic units and the length of the edge of the base is $6$ units. Substituting $\mathrm{2,880}$ for $V$ and $6$ for $s$ in the formula $V=s^{2}h$ yields $\mathrm{2,880}=\left(6^2\right)h$, or $\mathrm{2,880}=36h$. Dividing both sides of this equation by $36$ yields $80=h$. Therefore, the height, in units, of the prism is $80$.

Choice A is incorrect. This is the height, in units, of a right square prism where the length of the edge of the base is $6$ units and the volume of the prism is $144\sqrt{30}$, not $\mathrm{2,880}$, units.

Choice B is incorrect. This is the area, in square units, of the base, not the height, in units, of the prism.

Choice C is incorrect. This is the height, in units, of a right square prism where the length of the edge of the base is $6$ units and the volume of the prism is $864\sqrt{5}$, not $\mathrm{2,880}$, units.