luxurious:very expensive, beautiful, and comfortable
extravagant:1.spending or costing a lot of money, especially more than is necessary or more than you can afford
2.doing or using something too much or more than is necessary
3.if someone makes extravagant claims, promises etc, they make big claims or promises that are not true or real
4.very impressive because of being very expensive, beautiful etc
這樣比較直觀了吧，extravagant的詞義更加寬泛，luxurious詞義比較單壹。
PS：如果自己有壹定的英文基礎的話，查單詞最好還是直接看英文註解，配合給出的例句，能夠讓妳更加準確的理解這個詞在英語語系中的含義和用法。推薦朗文當代英語詞典（第四版）