maths question

Please look at the attachment.

My question is, if we were not told "where the last 8 people get off", would it then become ambiguous whether 1/3 of people go off or not on the fourth stop?

You have to have something that relates the fraction to an absolute number.
Note in this case it's easier to model that 2/3 remain on the bus each time, so it's a simple geometric sequence

I do very much agree with what you're saying. I have badly worded what I was asking, so I'll keep trying until you get what I mean.

I meant why can't we assume: for the 1st stop (2/3 of the original remain), 2nd stop (2/3 of the 1st remain), 3rd stop (2/3 of the 2nd remain), 4th stop (2/3 of the 3rd remain).

But I guess the fact that it says "where the last 8 people get off" tells us that at the 4th stop we are not going to do 2/3 of the 3rd stop as we would still have some people left. Therefore, we assume that at the 4th stop prior to people getting off there were 8 people and at the 3rd stop there must have been 12 people.

The question says that all 8 remaining people get off at the 4th stop, so that's 8/27 or (2/3)^3 of the original. The numbers work out nicely.
I think you're over thinking it a bit. The 2/3 rule finished after the third stop.

Also, we know the 2/3 rule stops on the 3rd stop because if it didn't then we would still have people on the bus after the 4th.

(I'm assuming this is an important point that I have mentioned because this is how we know the 2/3 rule finishes at the third stop).

Yes. I thought you were ok after your previous post?
The question could be a touch clearer, but it says all 8 people get off at the fourth stop, so the 2/3 rule must have finished at the previous one. It's fairly clear.