Step 1: Find the area of the rectangle

$$Areaofrectangle=width\times height$$

$$=6\times 4=24squareinches$$

Step 2: Find the area of the ellipse

$$a=\frac{Lengthofminoraxisofellipse}{2}=4÷2=2inches$$

$$b=\frac{Lengthoflargeaxisofellipse}{2}=6÷2=3inches$$

$$\therefore Areaofellipse=\pi ab=\pi \times 2\times 3=6\pi$$

Step 3: Subtract

$$\therefore Areaofshadedregion=24-6\pi$$