When I looked up the kanji for うける, I found both 受ける and 請ける. Denshi Jisho lists them with identical definitions and has examples using both as "accept" or "take".
I am curious which kanji is best for the sentence above, and if there is a general difference between 受ける and 請ける?
Sounds like a direct translation of "Do you accept credit cards?" I suspect the lesson wasn't written by a native speaker, or even a foreigner with much experience using Japanese.
I was asked to translate "do you/they accept credit cards?" The answer book gave "クレジットカードをうけますか" as the correct translation. I never saw that before so I looked up うける and found two forms: Find words - Denshi Jisho
If the answer book is wrong then that might be the source of the confusion.
From the merchant side, a store that advertises itself taking cards might be クレジットカードはご利用になれます。 or クレジットカードは利用いただけます :? although I doubt very much they would use the common forms of うける。