I don't understand why will only the 12 ohms lamps turn on when the switch is in position 2. shouldn't the current flow like this (like I highlighted in the picture)?

Current only flows from a higher voltage to a lower voltage. What you highlighted cannot happen because current cannot flow towards a lamp unless there is a lower voltage on the other side of it. The current will continue to the lower voltage of the battery instead.

Answer8.0m;