Translation:She teaches her dog to fetch the newspaper.
the ''correct solution'' says ''she teaches her dog to fetch the newspaper''. i'm a little confused why it's not ''the dog''. i don't see henne, or sin before hunden.
There can be more than one correct solution. I think by showing "her dog" as the default solution, they're trying to indicate that hunden doesn't always have to be "the dog", it just always has to be definitive, so one dog in particular, and "her dog" works equally well.
I agree it's a bit confusing the first time.
In which cases is 'lär ut' necessary? Only when it's ambiguous whether the subject is themselves doing the learning or the teaching? Like, 'hon lär svenska' would require either 'lär ut' or 'lär sig', but anything else?
To lära ut is necessary for teaching or making someone learn something. To lära sig is used for learning. Using lär on its own is uncommon.
To clarify: ut is necessary when what you teach is a noun, Hon lär ut svenska 'She teaches Swedish' but not used when it's a clause, like in this example.
I think both are transitive, it's just that lär ut is a particle verb that works a bit differently.
Lära can be used intransitively too, but in most cases the counterpart to to teach would be att undervisa instead.