"I can teach you everything."
Translation:Jeg kan lære dig alt.
Nogen lærer nogen noget = Someone teaches someone something/Jeg lærer jer dansk = I'm teaching you (all) Danish
Nogen lærer noget = Someone learns something/Jeg er ved at lære dansk = I'm learning Danish
In Danish, the word for "teach" and "learn" can both be "lære", it's just a matter of whether there is a second person involved or not (although it's not always the case, but just a general rule)
According to Den Danske Ordbog
No, not to mean the same. "At undervise" does mean "to teach" but it behaves differently, and the meaning/subtext would be different.
At lære - in Danish, means that someone learns what it is is being teached. So in "Jeg kan lære dig alting." - I can teach you everything. - the subtext is that "I" teaches "you" everything to the point that "you" knows and understands and can do whatever it is "I" is teaching.
At undervise - in Danish, means to teach, but it doesn't mean that anyone is learning. "Jeg kan undervise dig i alting." - I can teach you everything. - Here the subtext in Danish is that "I" can teach "you" all subject matters, but "at undervise" does not talk about the "you"'s understanding of the subject matter.
I'm relatively certain that the difference is the same with Lernen and Unterrichten, but my German is sketchy.
Hello and thanks for your detailed answer. After all, there are many differences between the languages that you don't know as a foreigner. -- Small information concerning german: "to learn"="lernen";"to teach"="lehren"="unterrichten" (with some grammar differences). -- Best wishes to you.