jmc

Each of the four shaded triangles in the diagram below has area $\frac{1}{2}(1)(3)=\frac{3}{2}$ square units, and the shaded triangles along with the hexagon form a rectangular region whose area is $6\cdot 4=24$ square units. Therefore, the area of the hexagon is $24-4\cdot \frac{3}{2}=\boxed{18}$ square units.