I've been given this question for homework, and I've made a bit of progress but I'm not sure what to do next. I called the intersection of the two lines $P$, and let $BP=x$ and $FP=y$. Thus, $PG=6-y$ and $PC=14-x$. I then used Power of a Point to get that $y=\frac{7x}{3}-\frac{40}{3}$, but I don't know where to go from here.