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The correct answer is $66$. It’s given that the right circular cone has a height of $22$ centimeters $\left(\text{cm}\right)$ and a base with a diameter of $6 \text{cm}$. Since the diameter of the base of the cone is $6 \text{cm}$, the radius of the base is $3 \text{cm}$. The volume $V$, $\text{in} {\text{cm}}^3$, of a right circular cone can be found using the formula $V=\frac{1}{3}\pi r^{2}h$, where $h$ is the height, $\text{in} \text{cm}$, and $r$ is the radius, $\text{in} \text{cm}$, of the base of the cone. Substituting $22$ for $h$ and $3$ for $r$ in this formula yields $V=\frac{1}{3}\pi {\left(3\right)}^2\left(22\right)$, or $V=66\pi$. Therefore, the volume of the cone is $66\pi {\text{cm}}^3$. It’s given that the volume of the cone is $n\pi {\text{cm}}^3$. Therefore, the value of $n$ is $66$.