jmc

Since $\alpha$ is inversely proportional to $\beta$, by definition $\alpha \beta =k$ for some constant $k$. Plugging in, we see that $(-3)\cdot (-6)=k$, so $k=18$. So when $\beta =8$, we have that $8\alpha =18$, or $\alpha =\boxed{\frac{9}{4}}$.