  The study of the Ashkin-Teller model (ATM) of spin-3/2 on a hypercubic
lattice is undertaken via Monte Carlo simulation. The phase diagrams are
displayed and discussed in the physical parameter space. Rich physical
properties are recovered, namely the second order transition and multicritical
points. The phase diagrams have been obtained by varying the strength
describing the four spin interaction and the single ion potential. This model
shows a new high temperature partially ordered phase, called $\langle S\rangle$
and a new Baxter 3/2 ground state which do not exist either in the spin-1/2 ATM
or in the spin-1 ATM.
