A 12V battery connected to a coil of resistance 6 Ω through a...

The current $\left(i\right)$ through the circuit is given by

$\begin{cases}i & = & \dfrac{V}{R} \\ & = & \dfrac{12V}{6Ω} \\ & = & 2A\end{cases}$

The formula to calculate the induced emf in the coil can be written as

$ε = L\dfrac{di}{dt} . . . \left(1\right)$

Substitute the values of the known parameters into equation (1) and solve to calculate the inductance of the coil.

$\begin{cases}20V & = & L \times \dfrac{2A}{1 \times {10}^{- 3}s} \\ & ⇒ & L = \dfrac{20V \times 1 \times {10}^{- 3}s}{2A} \\ & = & 10mH\end{cases}$