Bipartite Graphs and Matchings · Challenge problem

Men $A,B,C,D$ rank women $W,X,Y,Z$ as $A\!:\!X,W,Z,Y$; $B\!:\!W,Z,Y,X$; $C\!:\!Z,Y,W,X$; $D\!:\!Z,Y,X,W$. Women rank men as $W\!:\!A,C,D,B$; $X\!:\!C,A,B,D$; $Y\!:\!B,D,A,C$; $Z\!:\!B,C,A,D$. How many different stable matchings does this preference profile admit?