problem: Suppose $c$ and $d$ are inversely proportional. If $c=9$ when $d=8$, find the value of $d$ when $c=6$.
solution: If $c$ and $d$ are inversely proportional, then $c\cdot{d}=k$ (where $k$ is a constant). We know that $c=9$ when $d=8$, so $(9)(8)=k$ or $k=72$. When $c=6$, $(6)(d)=72$.  Thus, $d$ must be equal to $\frac{72}{6}$ or $\boxed{12}$.