Hi, Izzy—"She answered the question stupidly" means that she answered the question in a stupid manner ("stupidly" is a verb-phrase modifier), and "Stupidly, she answered the question" means it was stupid for her to answer the question, i.e., that she answered the question was stupid ("stupidly" is a sentence modifier). Interestingly, if "stupidly" is set off by a comma in the first sentence ("She answered the question, stupidly"), that sentence will have the same meaning as the second sentence ("Stupidly, she answered the question").
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