"The recepie" would be just "a receita". But the verb "gostar" (like) always asks for the preposition "de". You never use this verb without the preposition. In some verbs, not using the right preposition can change the meaning, just as it happens in English ("looking for" is different from "looking at") for exemple.
The preposition "de" is "part of the verb, and it combines with the article of the following word. So "gosta de + a receita" becomes "gosta da receita".
As far as I know, you can say both depending on the situation. Imagine you have some animals at home and you are talking about them to your friend, so you can say: Eu gosto dos animais. But to say that you like the animals as a general opinion, I think you should say: Eu gosto de animais.
"Eu gosto de animais" means "I like animals", so you're talking about animals in general. "Eu gosto dos animais" is "I like the animals".
Remember this: "de" is equivalent to "of" ------ "da" and "do" are equivalent to "of the" (feminine and masculine, respectively). And you you always use "de", "da" or "do" to link the verb "gostar" with the object
Think like this: sometimes you'll need to use the preposition "de" to indicate place, possession, because the verb is indirect transitive etc., as you can see in the sentence above; "gostar" is indirect transitive, so it asks necessarily for the preposition "de" with the object: - Você (subject) gosta (indirect transitive verb) de (preposition that "gostar" needs before its object) a receita (indirect object)?
In this case, the noun "receita" needs a specifier - which turns out to be the article "a", which is singular and feminine because "receita" is singular and feminine too. In this case, notice that the preposition "de" and the article "a" are together, so we always contract them in "da".
- Você gosta --> de a <-- receita?
- Você gosta (de+a) receita?
- Você gosta da receita?
This kind of contraction is very very very very common in Portuguese, so learn it well!
- Other possible common contractions and combinations:
de+o = do de+a = da de+os = dos de+as = das
a+o = ao a+a = à (this is called "crase") a+as = às a+os = aos
por+a = pela...
a+aquele = àquele...
You're correct. Every single time you use the verb "gostar", its object is introduced by the preposition "de", once "gostar" is indirect transitive. Actually, this rule applies to the verb; there is the noun "gosto" (it sounds like /gôsto/, not /gósto/) and it doesn't need the preposition "de".