Bati and Ertas [Physica B 513 (2017) 40] presented a study of dynamic magnetic hysteresis loop properties (DMHLFs) of a mixed spin (1/2, 1) Ising system (IS) on a hexagonal lattice within the mean-field theory based on the Glauber dynamics approach. They observed a number of interesting DMHLFs. We extended the investigation of DMHLFs of a mixed spin (1/2, 1) IS on a hexagonal lattice using the path probability method. We also examined the influences of the rate constants on DMHLFs as well as magnetic coercive fields and remanent magnetizations. We observed that some of our results are in quantitatively good agreement with some theoretical works on various ISs and experimental reported works on some magnetic materials as well as works within the melt-spinning method. We also found that the effects of rate constants are more effective on DMHLFs of the magnetization of spin-1 particles than loops of the magnetization of spin-1/2 particles.