jmc

Adding a couple lines, we have



The marked right triangle has a hypotenuse of $\sqrt{6^2+8^2}=10$, which makes the other (congruent) triangle a right triangle as well. The area of the entire figure is then the area of the rectangle added to the area of the two right triangles, or $12\cdot 8+2\left(\frac{6\cdot 8}{2}\right)=\boxed{144}$ square inches.