Step 1: Find the area of the rectangle

$$ Area\ of \ rectangle=width\times height $$

$$ =6\times4=24\ square\ inches $$

Step 2: Find the area of the ellipse

$$ a=\frac{Length\ of\ minor\ axis\ of\ ellipse}{2}=4\div 2\ =2\ inches $$

$$ b=\frac{Length\ of\ large\ axis\ of\ ellipse}{2}=6\div 2\ =3\ inches $$

$$ \therefore Area\ of\ ellipse = π a b=π \times 2 \times 3=6π $$

Step 3: Subtract

$$ \therefore Area\ of\ shaded\ region=24-6π $$