How to get the shaded region of the rectangle?
Hint:
there are eight small red triangles all with the same area
six of them are shaded
The area of hatched region of the rectangle is the area of the rectangle minus the sum of the areas of the right triangles $BEF$ and $DGH$. Now if you glue these triangles along their hypotenuses, you obtain a rectangle with dimensions half the dimensions of the big rectangle, hence with area equal to ¼ area of the big rectangle.
Hence the required area is ¾ big area, i.e. $\color{red}{48}$.
If you notice that if you combine two right triangles then they occupy the area of $\dfrac14$ of the total area.
So, the area of the shaded region is $=64-\dfrac14(64)=64-16=48$