Answer
$216\,nm$
Work Step by Step
The film thicknesses that causes constructive interference at wavelength $\lambda$ are
$d=\frac{\lambda m}{2n}$, $m=1,2,3,...$ and where $n$ is the index of refraction.
The thinnest film has $m=1$.
Its thickness is
$d=\frac{(600\times10^{-9}\,m)(1)}{2(1.39)}=216\times10^{-9}\,m=216\,nm$
