\(\left\{ \begin{array}{l}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{4}\\x+6=y\end{array} \right.\)
$⇔$\(\left\{ \begin{array}{l}\dfrac{1}{x}+\dfrac{1}{x+6}=\dfrac{1}{4}\\x+6=y\end{array} \right.\)
$⇔$\(\left\{ \begin{array}{l}x^2-2x-24=0\\x+6=y\end{array} \right.\)
$⇔$$\begin{cases}\left[ \begin{array}{l}x=6\\y=12\end{array} \right. \\\left[ \begin{array}{l}x=-4\\y=2\end{array} \right.\end{cases} $