  Using the Monte-Carlo method, we study the magnetic properties of the
Ashkin-Teller model (ATM) under the effect of the crystal field with spins $S =
1$ and $\sigma = 3/2$. First, we determine the most stable phases in the phase
diagrams at temperature $T = 0$ using exact calculations. For higher
temperatures, we use the Monte-Carlo simulation. We have found rich phase
diagrams with the ordered phases: a Baxter $3/2$ and a Baxter $1/2$ phases in
addition to a $\left\langle \sigma S\right\rangle$ phase that does not show up
either in ATM spin 1 or in ATM spin $3/2$ and, lastly, a $\left\langle
\sigma\right\rangle = 1/2$ phase with first and second order transitions.
