  Magnetic properties of a mixed spin-1/2 and spin-3/2 Ising model on honeycomb
lattice are investigated within the framework of an exact star-triangle mapping
transformation. The particular attention is focused on the effect of uniaxial
and biaxial crystal-field potentials that basically influence the magnetic
behaviour of the spin-3/2 atoms. Our results for the basic thermodynamic
quantities, as well as the dynamical time-dependent autocorrelation function
indicate the spin tunneling between the $| \pm \frac32>$ and $| \mp \frac12>$
states in two different magnetically ordered phases OP$_1$ and OP$_2$,
respectively.
