The dynamic behavior of a two-sublattice spin-2 Ising model with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field on a hexagonal lattice is studied by using the Glauber-type stochastic dynamics. The lattice is formed by alternate layers of spins sigma = 2 and S = 2. We employ the Glauber transition rates to construct the mean-field dynamic equations. First, we study the time variations of the average sublattice magnetizations to find the phases in the system, and the thermal behavior of the dynamic sublattice magnetizations to characterize the nature (continuous and discontinuous) of the phase transitions and to obtain the dynamic phase transition (DPT) points. Then, the behavior of the dynamic total magnetization as a function of the temperature is investigated to find the dynamic compensation temperatures as well as to determine the type of compensation behavior. We present the dynamic phase diagrams including the dynamic compensation temperatures in the nine different planes. Phase diagrams contain the paramagnetic (p), antiferromagnetic-1 (af(1)), antiferromagnetic-2 (af(2)) and ferrimagnetic (i) fundamental phases, five different mixed phases and the compensation temperature or the L-type behavior that strongly depend on the interaction parameters.