Translation:The restaurant has a big and a small kitchen.
Is Keuken "De" word? because "Grote" and " Kleine" both has -e ending?
In future if you are unsure you might want to look it up in an online dictionary. It's not perfect but Wiktionary (a dictionary/thesaurus sister site of Wikipedia) is generally a good starting point. The entry for keuken is here. You should see that it is listed as keuken f. The f tells you that it is feminine. Both masculine and feminine words are "de" words, while "het" words are neuter. (You should notice therefore that de is equivalent to German der and die, while het is equivalent to das).
I speak both Dutch (Belgian) and English (American:Californian:San Franciscan); both since childhood. You must understand that languages have flexibility. It would be perfectly acceptable to say, "Het restaurant heeft een grote keuken, en een kleine keuken" in Dutch, as well as to say, "The restaurant has a big and a small kitchen" in English. When you are discussing the same subject, in this case the kitchen, there is no need to repeat it in either language, although it is acceptable to do so in both languages.
I disagree. "A big and a small kitchen," is grammatically correct. It also sounds better to my Californian ears than repeating "kitchen" or using "one" to replace it.
If you are a native speaker and unsure about the correctness of "a big and a small," consider the following sentence: "The restaurant has two kitchens, a big and a small one." Does that not sound correct?
Agreed. Personally as a neutral Scottish English speaker I'd phrase it as "The restaurant has one large and one small kitchen" or possibly "… large and small kitchens" (although the latter would expand the possible meaning slightly to include >1 of either type).
"...a large and a small kitchen" doesn't sound wrong but it's not how I'd say it. When phrasing it like that I'd probably insert a both before the first a (i.e. "...both a large and a small kitchen"). Using big (rather than large) doesn't sound right to me in any of the formulations, but of course that doesn't make it wrong.
Perhaps it is a regional difference. Out of curiosity, I googled "a big and a small" and got 17,300,000 hits. One of them was an English lesson:
"You are going to fill a bag with objects. Get 2 of each object, but make sure one is bigger than the other. For example, a big and a small car, . . . ."
Here is the link: