Answer
$$\frac{8}{27}
.$$
Work Step by Step
Since $1 yd =36 in$, we have
$$
\frac{32 \ in}{3 \ yd}=\frac{32 \ in}{3\cdot 36 \ in}=\frac{4\cdot 8}{3\cdot 4\cdot 9}=\frac{8}{27}
.$$
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