We present a study, within a mean-field approach, of the kinetics of the mixed spin-1 and spin-3/2 Ising model with Fe4N structure in the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the mean-field dynamical equations. We investigate the time dependence of average magnetizations and the thermal behavior of the dynamic order parameters. From these studies, we obtain the dynamic phase transition (DPT) points and construct the dynamic phase diagrams (DPD) in different frequencies. Phase diagrams contain three mixed and four fundamental phases besides that many special points and reentrant behavior that strongly depend on interaction parameters.