$y=4-\frac{x^2}{4}$ and $y=\frac{x-4}{2}$

$$\begin{aligned} & \text { Area }=\int_\limits{-6}^4\left(4-\frac{x^2}{4}-\frac{x}{2}+2\right) d x \\ & =\left[6 x-\frac{x^3}{12}-\frac{x^2}{4}\right]_{-6}^4 \\ & =6(4+6)-\left(\frac{64}{12}+\frac{216}{12}\right)-\left(\frac{16}{4}-\frac{36}{4}\right) \\ & =60-\frac{70}{3}+5 \\ & \alpha=\frac{125}{3} \\ & 6 \alpha=6 \times \frac{125}{3}=250 \end{aligned}$$