"Does this restaurant take cash?"
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The word 家 has many uses, some of them related and some seemingly unrelated, but the use which is relevant here is as a classifier for shops and businesses. Some of the examples listed here (https://www.chiculture.net/0615/html/d13/0615d13.html) as nouns associated with the classifier 家 include hotel, restaurant, factory, theatre, hospital, and bank.
Classifier (also called a measure word and known in Chinese as 量詞 liàng cí) is a part of speech, like verb, noun, adjective etc. In this sentence 家 is performing the role of a classifier. This forum post is a nice, overview of some of the most common classifiers. https://forum.duolingo.com/comment/33611236