jmc

Multiplying all three gives equations gives us $$\frac{x}{y}\cdot \frac{y}{z}\cdot \frac{z}{w}=3\cdot 8\cdot \frac{1}{2}⟹\frac{x}{w}=12.$$ Taking the reciprocal of both sides of this equation gives $w/x=\boxed{\frac{1}{12}}$.