Given $\lim_{ x \rightarrow 4 } {f(x) = 7}$ and $\lim_{ x \rightarrow 4 } {g(x) = 4}$, evaluate $$\lim_{ x \rightarrow 4 } \frac{g(x) - f(x)}{6 g(x)}.$$

If the limit does not exist enter DNE.

Limit =