The verb know is a stative verb, describing a state of mind or being, and is not typically used in the continuous tense (e.g., was knowing).
Option (C) corrects this by using the simple past knew, which matches the past-tense context of didn't speak and conveys that she possessed knowledge at that time.
Option (A) uses knows (present tense), creating a tense mismatch with didn't speak (past tense).
Option (B) incorrectly uses was known, a passive voice construction implying someone else knew her, not that she knew the answer.
Option (D) uses had know, which is grammatically incorrect; the correct past perfect form is had known, but it’s less suitable here since there’s no earlier past event to justify the past perfect.
Thus, (C) is the grammatically and contextually correct choice.