jmc

We begin by multiplying the first equation by 2, giving us a system of two equations $$\begin{array}{rl}2d-12c& =8\\ 2d-9c& =20\end{array}$$From here, we can subtract the second equation from the first. This gives us $(2d-12c)-(2d-9c)=8-20$, which simplifies to $-3c=-12$ or $c=4$. Since we now know the value of $c$, we can plug this back into the first equation to solve for $d$. This gives us $2d-12(4)=8$, or $2d=56$ and $d=28$. Since $d=28$ and $c=4$, $\frac{d}{c}=\frac{28}{4}=\boxed{7}$.