jmc

Simplifying the left side gives $$\frac{1\frac{1}{6}}{w}=\frac{\frac{7}{6}}{w}=\frac{7}{6}\cdot \frac{1}{w}=\frac{7}{6w},$$ so the equation is $$\frac{7}{6w}=\frac{42}{3}=14.$$ Multiplying both sides by $6w$ gives $7=14(6w)$. Dividing both sides by 7 gives $1=2(6w)$, and dividing both sides by 12 gives $w=\boxed{\frac{1}{12}}$.