1. **State the problem:** We have a circle with radius 4 units and a shaded sector of 270°. 2. **Formula for area of a sector:** The area $A$ of a sector with radius $r$ and central angle $\theta$ (in degrees) is given by $$A = \frac{\theta}{360} \times \pi r^2$$ 3. **Calculate the area of the shaded sector:** Here, $r=4$ and $\theta=270$. $$A = \frac{270}{360} \times \pi \times 4^2 = \frac{270}{360} \times \pi \times 16$$ 4. **Simplify the fraction:** $$\frac{270}{360} = \frac{\cancel{270}}{\cancel{360}} = \frac{3}{4}$$ 5. **Calculate the area:** $$A = \frac{3}{4} \times \pi \times 16 = 12\pi$$ 6. **Final answer:** The area of the shaded sector is $$12\pi$$ square units.