The volume \( V \) of a rectangular pyramid can be calculated using the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
First, we need to calculate the base area of the rectangular pyramid. The base area \( A \) is given by:
\[ A = \text{width} \times \text{length} = 7 , \text{mm} \times 12 , \text{mm} = 84 , \text{mm}^2 \]
Now we can plug the base area and the height into the volume formula:
\[ V = \frac{1}{3} \times 84 , \text{mm}^2 \times 8 , \text{mm} \]
Calculating the volume:
\[ V = \frac{1}{3} \times 84 \times 8 = \frac{1}{3} \times 672 = 224 , \text{mm}^3 \]
Thus, the volume of the rectangular pyramid is
\[ \boxed{224} , \text{cubic millimeters}. \]