To find the value of \( DP \) in triangle \( DRP \) where \( RP = 12 \) and \( DR = 16 \), we can use the Law of Cosines if we have the included angle, or we can apply the concept of triangular proportions if applicable.
However, since there is no specific angle provided, we might suspect that the triangle could be a right triangle or might have special properties.
If we assume it is a right triangle, we can apply the Pythagorean theorem:
\[ DP^2 = DR^2 + RP^2 \]
Substituting the known values:
\[ DP^2 = 16^2 + 12^2 \] \[ DP^2 = 256 + 144 \] \[ DP^2 = 400 \] \[ DP = \sqrt{400} = 20 \]
Thus, the value of \( DP \) is \( 20 \).
Therefore, the answer is \( \boxed{20} \).