I don't think she can answer.

Literal

She [topic-は] answer-can-not [quotative-と] think.

答えられない uses the potential form of 答える — 'cannot answer.' The polite ~と思います wraps the speaker's opinion. Japanese structures this as 'she cannot answer, I think' (negative inside the quote, polite verb outside), while natural English inverts to 'I don't think she can answer' — a standard translation shift between the two languages.