Answer
$R = 750~\Omega$
Work Step by Step
We can find the equivalent resistance $R_{eq}$:
$\tau = \frac{L}{R_{eq}}$
$R_{eq} = \frac{L}{\tau}$
$R_{eq} = \frac{7.5\times 10^{-3}~H}{25\times 10^{-6}~s}$
$R_{eq} = 300~\Omega$
We can find $R$:
$\frac{1}{R_{eq}} = \frac{1}{500~\Omega}+\frac{1}{R}$
$\frac{1}{R} = \frac{1}{R_{eq}} - \frac{1}{500~\Omega}$
$\frac{1}{R} = \frac{1}{300~\Omega} - \frac{1}{500~\Omega}$
$\frac{1}{R} = \frac{5}{1500~\Omega} - \frac{3}{1500~\Omega}$
$\frac{1}{R} = \frac{2}{1500~\Omega}$
$R = \frac{1500~\Omega}{2}$
$R = 750~\Omega$
