"Please tell me the meaning of this word."
I feel like this should be 教えて/おしえて? こたえ as far as I know is more "answer [this question]" where as 教える is more of a general "instruct" or "explain" this.
答える doesn't use the を particle. It makes sense but it's grammatically wrong.
Maybe 答える is used transitively (using を) from time to time irl though it technically is an intransitive verb. I don't know.
The correct particle is に. We can use that when we are answering TO a question.
こたえ because this is in the context of a classroom. This is how a teacher would ask a student to answer a question in front of the class. It's also how the host of a quiz show would ask contestants. 教え would be if you don't know the meaning and want someone to teach you. Of course, on Duo the context is uncertain so both should probably be accepted.