[tex]\Delta FGH\sim\Delta LMN[/tex], so corresponding sides occur in some ratio with one another. In particular, the order the vertices tells you that
[tex]\dfrac{FG}{LM}=\dfrac{GH}{MN}=\dfrac{HF}{NL}[/tex]
[tex]\implies\dfrac{FG}{14}=\dfrac{54}{12}[/tex]
[tex]\implies FG=\dfrac{14\cdot54}{12}=63[/tex]
