To determine the volume of the rectangular prism after a dilation with a scale factor of 4, we first need to find the original volume of the prism with dimensions 2 m, 3 m, and 4 m.
The volume \( V \) of a rectangular prism is given by the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Substituting the given dimensions:
\[ V = 2 , \text{m} \times 3 , \text{m} \times 4 , \text{m} = 24 , \text{m}^3 \]
When a three-dimensional shape like a rectangular prism is dilated by a scale factor \( k \), the volume is affected by a factor of \( k^3 \):
\[ \text{New Volume} = \text{Original Volume} \times k^3 \]
Here, the scale factor \( k = 4 \):
\[ k^3 = 4^3 = 64 \]
Now to find the new volume:
\[ \text{New Volume} = 24 , \text{m}^3 \times 64 = 1536 , \text{m}^3 \]
Therefore, the volume of the rectangular prism after dilation is:
\[ \boxed{1,536 , \text{m}^3} \]
This matches option d.