A theoretical description of the six-wave mixing spectroscopy is presented. The six-wave mixing spectroscopic signals in time and frequency domains are expressed in terms of the fifth-order nonlinear response functions. Particularly, the resonant coherent hyper-Raman scattering with wave vector of 4k(1)-k(2) and frequency of 4 omega(1)-omega(2), where 2 omega(1) approximate to omega(2) is discussed by invoking the optical Bloch approximation. The coherent anti-Stokes hyper-Raman scattering (CAHRS) susceptibility is found to be very similar to that of CARS. The dephasing-induced vibrational resonance in the excited state is also manifest in this experimental configuration. By making a direct comparison of CAHRS signal with that of CARS, it is found that the ratio of CAHRS to CARS susceptibilities provides a crucial information on the permanent dipole moment of the excited state in either gas or condensed phases. It is briefly discussed that this method can be of use in estimating the molecular hyperpolarizability.