"I like having breakfast at home."
Translation:Я люблю завтракать дома.
"Дома" (with the stress on "о") is an adverb of location that translates as "at home," and is not used with prepositions.
This contrasts with the the Russian noun "дом," which translates as "house." So, "в доме" is "in [the/a] house" (prepositional case, singular), while "в дома" (stress on "а") would be "to [the] houses" (accusative case, plural).
"Дома" with the stress on "о" is also the genitive singular of "дом," but this would not be used with the preposition "в"
It really irks me sometimes how the hint system is pretty much useless. I put down "Мне нравится завтрак дома", having forgotten the word for breakfast. My suggestions were "завтрак", "завтраком", and "завтрака". The correct answer is obviously завтракать, and I accept that I was wrong, but having the hint system give me three completely wrong answers is unacceptable. This happens on other answers too - I often finding myself skipping just so I can get the right answer and not have to deal with incorrect suggestions.
If they suggested the exact translation for each part of the sentence, it would be easier for the users to finish the exercises by simply copying... without eventually learning anything. This way, they only give you, in fact, a "hint", so that you can, with a little effort, memorise the words more effectively.
Let's break down your sentence: Я люблю¹ / иметь завтрак² / в дома³.
1 - Я люблю
2- иметь завтрак
You used the verb име́ть here. It means "to have/possess". Would you ever say "I like possessing breakfast"? Sounds weird. Breakfast is not something we could refer to as possible of being possessed. We must understand "to have breakfast" as an unity which carries only one meaning. This meaning can be translated into russian as "за́втракать". Therefore "I have breakfast" or "I am having breakfast" can be translated as "я за́втракаю".
3- в дома
"At home" can be simply said by using the word "дома". When we use preposition "в" + noun in acusative, it indicates motion towards somewhere. It may be hard to understand now and it is not the point of this lesson.
I'll concede the в дома part (although it would seem that this follows the rules of prepositional case); but why is иметь included in the hints if it should not be used in the translation? Obviously "to possess breakfast" is an unnatural construction even in English, but someone learning Russian would be led to believe that "to have breakfast/lunch/dinner/a sandwich" is an acceptable phrase. If not, there should not be separate drop-down hint for "to have/having" but simply завтракать, in the manner that words are lumped in other exercises - e.g., "domestic animal" (don't recall the Russian) = "pet".
"В дома" does not follow the rules of prepositional case. If it did, it would be "в доме" instead. Unfortunately I cannot make any considerations about the inclusion of иметь in the hints. I am just a regular user who has no ideia about how the developers create the hints lists. It is true that beginner students like us might be led to believe that иметь should be used in the construction of this sentence, when actually it should not. But since mistakes are an essential part of the learning process, le't not blame them, but praise them :)