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Multiplying all three gives equations gives us $$\frac{a}{b}\cdot \frac{b}{c}\cdot \frac{c}{d}=4\cdot \frac{1}{3}\cdot 6,$$so $$\frac{a}{d}=8.$$ Taking the reciprocal of both sides of this equation gives $d/a=\boxed{\frac{1}{8}}$.