Fixed. Thank you!

It can be written both ways.

There are 2 ways for counting:

1. Noun + number + counter 사람 다섯 명

Or

1. Number + counter의 + Noun 다섯 명의 사람

It wants "in" instead of "at". I reported it as a correct answer.

We just realised that this sentence isn't in the past tense, so we added a new exercise with the particle -었-, and your answer in the past form "Eight women were at the hospital." will be accepted there. Thank you! :)

It is not the possessive particle, just like the English word of. 여덟 명의 여자 literally means 8 units of women. However, just like most other cases, you can drop 의 though it's usually not dropped when the counter is of one syllable.