解：
因为
$(\dfrac{1}{6}-\dfrac{2}{7}+\dfrac{2}{3}-\dfrac{3}{14})÷(-\dfrac{1}{42})=(\dfrac{1}{6}-\dfrac{2}{7}+\dfrac{2}{3}-\dfrac{3}{14})×(-42)$
$=\dfrac{1}{6}×(-42)-\dfrac{2}{7}×(-42)+\dfrac{2}{3}×(-42)-\dfrac{3}{14}×(-42)$
$=-7 + 12 - 28 + 9$
$=-14$
所以$(-\dfrac{1}{42})÷(\dfrac{1}{6}-\dfrac{2}{7}+\dfrac{2}{3}-\dfrac{3}{14})=-\dfrac{1}{14}$
