I'll get off at the next station
to get down (at least in BE) has got two quite different meanings
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IŽll get off/down at the next station.
Which preposition shall I use in the case?
I AM NOT A TEACHER BUT HOPE THIS MIGHT HELP YOU OUT.
Get down at the next station .
more examples... where will you get down.
Usage of "get down":
"I managed to get down that revolting medicine" >> I managed to swallow that revolting medicine.
"Make sure you get down what is said during the meeting" >> Make sure you have noted/written down ...
"It was very difficult to get down from the high wall" >> It was very difficult to descend...
I'll get off at the next station, buy something at the grocery store, and walk home.
Do you 'change' a bus / tram / tube / train if you have to get off at one station to take another bus / tram etc.?
You might not be getting off if you dropped off just before the station.
Also you might not be getting off at the next one too.