"Anybody didn't come to the meeting" is impossible in English. The answer key was wrong. Only "somebody" makes sense in this context.
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The sentence you quoted just sounds strange with 'anybody' at the beginning.
You could say:
Nobody came to the meeting.
but:
Anybody didn't come to the meeting. - sounds incorrect to me.
Somebody didn't come to the meeting. would imply that someone you'd expected to turn up didn't. In other words e.g. not all the people who were invited came to the meeting.