Final answer:
The phrase 'Lucy didn't notice Jillian entering' means that Lucy was unaware of Jillian's arrival as she did not see her come in. Choice a) is the correct answer, indicating Lucy's lack of awareness of Jillian's entry.
Step-by-step explanation:
The student asked the following question: What does the phrase 'Lucy didn't notice Jillian entering' mean? The correct choice is a) Lucy didn't notice Jillian entering. This means that Lucy was not aware of Jillian's arrival or the act of her coming into a place because she didn't see it happen. It does not imply that Lucy saw Jillian enter (choice b), that she is asking for clarification (choice c), or that she is talking about someone else (choice d). The main answer to this question is based on understanding context clues and the implied meaning of phrases in English.