Trying to solve a RL circuit by hand but simulator calculates a value I do not understand
I give you a tip. 
Before the switch is close the is a current in the inductor. 
And this current is equal to  \$I_L =\frac{20V}{200\Omega} = 100\textrm{mA} \$

So at the very first moment of time (t=0) when we closed the switch. 

The equivalent circuit looks like this: 







simulate this circuit &ndash; Schematic created using CircuitLab

As you can see I replace an inductor with a current source. Because this is how the inductor will behave at time t = 0 when you closed the switch. 
because the inductor current cannot change instantaneously. 

And if you do the calculation you will get that the voltage at the \$V_X\$ node is indeed equal to \$-12V\$ 

And the circuit time constants is \$ \tau = \frac{L}{R_1||R_2}\$.