The adjacent sides of a parallelogram are 32 cm and 24 cm.

Longer side = 32 cm
Shorter side = 24 cm
Let the distance between the shorter sides be x cm.

Area of a parallelogram = Longer side $\times$ Distance between the longer sides

$=$ Shorter side $\times$ Distance between the shorter sides

or, $32 \times 17.4=24 \times x$

or, $x=\frac{32 \times 17.4}{24}=23.2 \mathrm{~cm}$

∴ Distance between the shorter sides = 23.2 cm