$\begin{aligned} & \int_{-\pi / 2}^{\pi / 2} \sin ^4 x \cos ^6 x d x=2 \int_0^{\pi / 2} \sin ^4 x \cos ^6 x d x \\ &=\frac{2 \frac{4+1}{2} ! \frac{6+1}{2} !}{2 \frac{4+6+2}{2} !} \\ &=\frac{\frac{3}{2} \cdot \frac{1}{2} \sqrt{\pi} \cdot \frac{5}{2} \cdot \frac{3}{2} \cdot \frac{1}{2} \cdot \sqrt{\pi}}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}=\frac{3 \pi}{256}\end{aligned}$