Hey Ahasueros.

If each switch is independent from the other (i.e. changing one switch doesn't impact the others in any way), then you multiply the combinations.

Since you have three positions for two switches the combinations for this are 3*3 = 9. Now you have another switch which has two choices which is independent from the others so multiplying gives 9*2 = 18.

I'm not quite sure why you did 2^3 if you know that each switch has three choices (i.e. the positions).

Intuitively another way to do think about this multiplication is to think of creating one "super switch" with all possibilities. So for a single 2-state 2-switch system you have {Off,Off}, {Off,On}, {On, Off], {On, On} so you could replace this set of two switches with one "super switch" with four possibilities.