The volume \( V \) of a right rectangular prism can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Plugging in the values for length, width, and height:
\[ V = 12 \times 5 \times 10 \]
Calculating this step by step:
\[ 12 \times 5 = 60 \]
\[ 60 \times 10 = 600 \]
Therefore, the volume of the right rectangular prism is:
\[ \boxed{600} \text{ units cubed} \]