I think 'I love putting/placing things in the house' should also be accepted.
The exercise is about infinite forms. Putting and placing are present participles, not infinitive forms of the verbs.
It's about Danish infinitive forms, not English ones. If the English gerund expresses the same idea as the Danish infinitive, and in a natural way, then it's a fine translation. Grammatical forms in different languages don't always correspond perfectly to each other.
I understand what you're saying, and I agree that understanding general meaning can be good enough when studying a foreign language. However, I do find it valuable that this program forces you to know the exact meaning of words. That's what this is testing and that's why the corrections can be a little strict. Especially when you're just starting out with a language, it's probably better to memorize exact meanings. I would agree with you if you were arguing for amazing and awesome to be interchangeable, for example. But with conjugation, because different tenses can mean different things, it makes sense for duolingo to be precise.
Sorry for the long reply. I get your point too, but I'm thankful that duolingo is picky so I know EXACTLY what words mean. I'm also a lover of grammar :)
But if you learn that the Danish infinitive only ever means the same as the English infinitive, then you haven't learnt exactly what the Danish infinitive means. Part of learning another language is learning both where it overlaps with English and where it differs from it, and accepting those differences even if they make things seem confusing at first. It's tempting to look for an 'exact meaning' when translating from one language to another, but more often than not it's more complicated than that. Being overly precise may seem helpful because it's easier to organise things in your head on a one-to-one basis, but it doesn't help you learn the language in the long run. Ultimately, being marked wrong for translating a sentence in a completely natural way is unhelpful and not at all precise.
Acha16: While I agree with you in that the more literal translation is probably more instructive and helpful (especially when I am prompted to translate from English to Danish), I see the problem in the inconsistency.
In some cases you have to give the literal cumbersome translation because nothing else is accepted while in others you need to only convey the gist in some form and you're fine. I assume that initially only the literal translations are accepted and it's completely fine for the basic tasks. Then, as the course develops, more complex grammatical constructions appear and the translations have to become looser. Then the course gets to idioms which are yet another can of worms. Later the looser translations seep down to the more basic exercises as well, but not uniformly and that is the cause of frustration. This is exacerbated by doing multiple languages which have different takes on this.
You can argue, that allowing looser translations might lead you astray because where do stop eventually? However, I think having the English sentence you have to translate to Danish be more instructive but accepting more translations from Danish to English would be a good compromise.
It's a matter of opinion. I don't really see the importance of focusing on the English translation sounding natural when English isn't the language being studied. Personally I like a teaching structure in which I'm told exactly what something means word for word, and then told what the meaning of the sentence as a whole is. By that I mean that in this example, I like to know that the sentence means, precisely " I love to place things in the house." and that this is how to convey "I love placing things in the house" in Danish. In a classroom setting, you can get both side by side, but with an app, it makes sense to choose only one translation. I'd rather know the exact meaning of the words, because that gives me a better contrast of how the structure is different in the two languages. To me saying that "elsker at placere ting" means "love placing things" is incomplete. The explanation that it means "love to place things" and this is how to convey "love placing things" in Danish in a natural way, makes more sense. To be fair, duolingo isn't really consistent on which version of the translation they accept. Either way it's an imperfect program, and the answers can sometimes be unsatisfying. Let's just agree to disagree.