I believe this is another case of the Norwegian V2 word order: https://en.wikipedia.org/wiki/V2_word_order#Swedish,_Danish,_Norwegian,_Faroese
That would be a different sentence, referring to a specific set of things. The example sentence is talking about "things like that" which is a more general class than just "those things".
In English we could also say "those kinds of things" or "that kind of thing". And then we have a shortcut where we sometimes say "those things" but we really mean "those kinds of things" or "that kind of thing". But that would be a lot of nuance to ask the Norwegian course to accept it as a translation and could be misleading to learners who are still weak on English.
I take this sentence to mean that someone is commenting disapprovingly on something that is being done (like sleeping in class) and saying "Things like that" [which you are doing] "you can do at home" [and not here]. I have no problem with this meaning. It is quite different from the sentence without the word like.