An inductor coil stores 64J of magnetic field energy and dissipates...

Energy stored in an inductor, $U = \dfrac{1}{2}L{I}^{2}$
$⇒ 64 = \dfrac{1}{2}L ( 8{)}^{2} ⇒ L = 2H$
and power dissipated in a resistor, $P = {I}^{2}R$
$⇒ 640 = ( 8{)}^{2}R ⇒ R = 10Ω$
Time constant of the $LRDC$ circuit is,
$τ = \dfrac{L}{R} = \dfrac{2}{10} = 0 . 2s$