Using the mixed-spin system, we precisely calculate the dynamic critical phenomena, namely
dynamic compensation behaviors, dynamic phase diagrams and dynamic hysteresis loops in a
multilayer Ising system that composes of four monoatomic layers. As the method, we use the
mean-field theory based on Glauber-type stochastic dynamics. It is found that the Hamiltonian
parameters have a strong effect on the dynamic critical phenomena. The system displays the P-,
Q-, R-, and S-type compensations and multiple hysteresis loop behaviors. The results are qualitatively
consistent with those of some theoretical and experimental studies.