The current in a LR circuit build up to $\frac{3}{4}\mathrm{th}$ of its steady state value in 4 sec. The time constant of this circuit is

$i=i_0\left(1-e^{\frac{-t}{\lambda }}\right)$

$\frac{3}{4}{i}_0=i_0\left(1-e^{\frac{-t}{\lambda }}\right)$

At    t = 4 sec $\to e^{\frac{-4}{\lambda }}=\frac{1}{4}$

$\begin{array}{l}\frac{4}{\lambda }={\log }_{e}4\Rightarrow \frac{4}{\lambda }=2={\log }_{e}2\\ \lambda =\frac{2}{\log 2}\Rightarrow \lambda =\frac{2}{ln2}\sec \end{array}$