Number of Elastic Constants for Completely Anisotropic Elastic Material
The number of elastic constants for a completely anisotropic elastic material can be determined based on the material's symmetry and the number of independent components in the stress-strain relation.

Hooke's Law for Anisotropic Materials
In the case of anisotropic materials, Hooke's Law can be expressed in matrix form as:
\[ \begin{bmatrix} \sigma_{11} \\ \sigma_{22} \\ \sigma_{33} \\ \sigma_{23} \\ \sigma_{13} \\ \sigma_{12} \end{bmatrix} = \begin{bmatrix} C_{11} & C_{12} & C_{13} & C_{14} & C_{15} & C_{16} \\ C_{21} & C_{22} & C_{23} & C_{24} & C_{25} & C_{26} \\ C_{31} & C_{32} & C_{33} & C_{34} & C_{35} & C_{36} \\ C_{41} & C_{42} & C_{43} & C_{44} & C_{45} & C_{46} \\ C_{51} & C_{52} & C_{53} & C_{54} & C_{55} & C_{56} \\ C_{61} & C_{62} & C_{63} & C_{64} & C_{65} & C_{66} \end{bmatrix} \begin{bmatrix} \varepsilon_{11} \\ \varepsilon_{22} \\ \varepsilon_{33} \\ 2\varepsilon_{23} \\ 2\varepsilon_{13} \\ 2\varepsilon_{12} \end{bmatrix} \]

Number of Elastic Constants
For a completely anisotropic material, there are 21 independent elastic constants. This is because there are 6 independent components of stress and 6 independent components of strain, giving a total of 36 components in the stiffness matrix. However, due to the material symmetry, the number of independent elastic constants reduces to 21.
Therefore, the correct answer to the question is option C, which states that there are 21 elastic constants for a completely anisotropic elastic material following Hooke's Law.