What is the area in square units of the quadrilateral $XYZW$ shown below?
We complete the figure to form a rectangle, as shown below, in which the two shaded areas are congruent right triangles.
[asy]
draw((0,0)--(3,0)--(3,72)--(0,45.6)--cycle,linewidth(1.5));
fill((0,0)--(3,0)--(3,4/3)--(0,4/3)--cycle,gray(0.7));
fill((0,45.6)--(1.2,45.6)--(1.2,72)--(0,72)--cycle,gray(0.7));
label("Y",(0,45.6),W);
label("Z",(0,0),W);
label("W",(3,0),E);
label("X",(3,72),E);
label("2",(1.5,0),S);
label("4",(0,22.8),W);
label("3",(3,36),E);
[/asy]
We constructed a $4$- by $3$-rectangle directly below the original quadrilateral, so the rectangle has an area of $4\times 3=12$ square units. Each shaded right triangle has base $4$ and height $3,$ so each has an area of $(1/2)(4)(3) = 6$ square units, making the total area of the shaded regions $2\cdot6=12$ square units.
[asy]
fill((0,0)--(0,72)--(1.2,72)--(1.2,0)--cycle,gray(0.7));
fill((1.2,0)--(3,0)--(3,4/3)--(1.2,4/3)--cycle,gray(0.7));
draw((0,0)--(3,0)--(3,72)--(0,72)--cycle,linewidth(1.5));
[/asy]
Since the shaded regions are congruent and have the same total area as the rectangle, the shaded regions must each have an area of $12/2=\boxed{6}$ square units.