The volume \( V \) of a rectangular pyramid can be calculated using the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
In this case, the base area \( A \) is calculated as:
\[ A = \text{Length} \times \text{Width} = 4 , \text{cm} \times 3 , \text{cm} = 12 , \text{cm}^2 \]
Now we can substitute the values into the volume formula:
\[ V = \frac{1}{3} \times 12 , \text{cm}^2 \times 12 , \text{cm} \]
Calculating this gives:
\[ V = \frac{1}{3} \times 144 , \text{cm}^3 = 48 , \text{cm}^3 \]
Thus, the volume of the rectangular pyramid is \( \boxed{48} , \text{cm}^3 \).