I have not used spacecurve before in Maple, but looking at help, I think you need to do this.
restart;
f:=(x,y)->2*x^2+3*y^2-x*y-6;
subs([x=1,y=1],diff(f(x,y),x));
subs([x=1,y=1],diff(f(x,y),y));
p1:=plot3d(f(x,y),style=patchcontour):
p2:=plots:-spacecurve([x,1,f(x,1)],x=-10..10):
p3:=plots:-spacecurve([1,y,f(1,y)],y=-10..10):
plots:-display([p1,p2,p3])