Find the volume of the right rectangular prism packed with 12 cubes. Each cube has an edge length of 12 inch.

Each cube has a volume of $(12\text{ in.})^3=1728\text{ in.}^3$. If there are $12$ cubes, then the total volume is $12\times 1728=20736\text{ in.}^3$. Thus, the volume of the right rectangular prism is $\boxed{20736\text{ in.}^3}$.