Closing the switch turns the output node into an ideal low node and sets the pull-up current. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Closing the switch gives a path to ground
The closed switch connects the output node to the return node, so the ideal output voltage is 0 volts.
Vout=0V
The pull-up current is exact
The source is 12 volts and the pull-up is 6 ohm, so the current is 2 amperes.