Answer
$t = 8.45~ns$
Work Step by Step
Note that the final value of the current is $\frac{\mathscr{E}}{R}$
We can find $t$:
$i = \frac{\mathscr{E}}{R}~(1-e^{-tR/L})$
$0.800 =(1-e^{-tR/L})$
$e^{-tR/L} = 0.200$
$e^{tR/L} = 5.00$
$\frac{t~R}{L} = ln(5.00)$
$t = \frac{L}{R}~ln(5.00)$
$t = (\frac{6.30\times 10^{-6}~H}{1200~\Omega})~ln(5.00)$
$t = 8.45~ns$
