In this case, if you got it correct and there is no additional correct answer, you just see that it is correct. If you happen to get it wrong, you will see one or more possible correct answers. Often, some correct answers will seem idiomatic, or colloquial, and you may not have ever considered them as possibilities.
I wish it were possible to separate fun and social comments from linguistic comments. I just want to know in what context this sentence would be used and there are so many social comments, it is difficult to find my answer. This sentence keeps coming up and it would only be used in English in rare situations, e.g. They give food to the poor. Why do we get this one so often?
In Standard American English, I think there is a subtle difference between the two phrasings. "They don't give food" makes them sound selfish. "They give no food" sounds like they have particular reasons for not giving food, or maybe they give something other than food. I don't think the subtlety of these meanings would translate to Spanish where (correct me if I'm wrong) the "No" always comes before the verb.
Goodness! They can't provide the complete context in which the sentence would be used. As another poster mentioned, consider these sentence fragments that can be string together to communicate a complete thought. "They don't give food" is correct in grammar and syntax. No, it may not be a sentence that you use in everyday life, but learning the structure of the sentence will provide a springboard for communicating more complex ideas, e.g., "They don't give food for free" or if you're really thinking outside the box "They don't give wine to children"
Further, the inferred intent of the sentence changes when you negate the verb vs negating the object. Is the purpose to highlight what the object that they don't give or the act of not giving. These would have slightly different nuanced meanings
"They don't give food to us" = "Ellos no nos dan comida" // "No dan comida" is a general statement, it means they do not give food to anyone. It could be said, for example, if you are talking about charity: "yo no doy dinero" = "I do not give money (to charity, in this example)". I hope it makes sense!
(I believe that) words pass through languages orally, independently of script. Hindi is in the so-called Indo-Iranian family of languages, as are English and all the Romance languages.
Consider Urdu and Hindi: two languages with very different scripts, and yet massively similar vocabulary.
Or consider Turkish before and after they changed alphabets :)