neither and possessive pronouns or adjectives

Neither of the women knew that…CEO had decided to retire.
a.their or b.her

i know that neither goes either singular or plural verb.whatever is right.So what about possessive pronouns and adjectives?They follow the same rules like someone,anyone etc?Thank you in advance for your replay.

There are two women, so you need to use ‘their’.

SOMETHING MORE.that vacation was the most fun time i have ever had or the funniest.

Your request above isn’t very clear. I suggest wording it like this (also not the capital for the pronoun ‘I’):

Another question:
“That vacation was the most fun time I have ever had” or “that vacation was the funniest time I have ever had.”

Although both could be correct, they carry different meanings and the one you are likely to want is ‘most fun time’ (meaning, ‘most enjoyable time’) ‘Funniest’ would indicate that it was humorous rather than that it was enjoyable.

Thank you a lot for the clarification of my questions.