smc

We draw in the rectangle bounding the given quadrilateral and label the points as shown. The area of rectangle $ABCD$ is $(3)(4)=12$, while the areas of the triangles $AEH$, $EBF$, $FCG$, and $GDH$ are, respectively, $$\begin{array}{rl}& \text{area of }△AEH=\frac{1}{2}(1)(2)=1,\\ & \text{area of }△EBF=\frac{1}{2}(3)(2)=3,\\ & \text{area of }△FCG=\frac{1}{2}(1)(1)=\frac{1}{2},\text{ and}\\ & \text{area of }△GDH=\frac{1}{2}(3)(1)=\frac{3}{2}.\end{array}$$ Hence the area of the given quadrilateral $EFGH$ is $12-\left(1+3+\frac{1}{2}+\frac{3}{2}\right)=\boxed{6}$.