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.