After people examined her claims, she had trouble maintaining her Choose

Choose ...

creditable

credibility

credible

credibly

credibility

Explanation:

If we look at sentence, we can see that a Noun is needed to complete the sentence. Basic structure of sentence is Subject+verb+object

here sentence second part is she had trouble maintaining her ...

here object which is noun is missing.

creditable means any action which can be praised. it is adjective so it is wrong option

credible is something which is convincing enough to be believed. Hence it is wrong as it adjective.

credibly is manner in which someone says or does something so that other person believe or is convinced with him.

Hence Credibility is correct as it is noun and talking about quality of being trustful and believable.