The family members arrived at the guest house______ a taxi.

The correct answer is: in

Various uses of preposition with "Taxi" : 
- We say get in a taxi. 
- We don't say get on a taxi

We say: get out of a taxi:
we don't say: get off a taxi

Also,
- We say that someone is in a taxi.
- We go somewhere by taxi.

Source: Oxford Learners Dictionary