"The boy can't think near the girl."
Translation:Drengen kan ikke tænke nær pigen.
Apparently the sentence is ambiguous. Even the hints give ved AND naer as correct solutions. Maybe naer is closer to the meaning intended, but in case ob ambiguity both answers should qualify as correct. In fact, I cannot see, how a discussion of naer ved vs. naer should apply here. Rune‘s posting is not at all helpful in this context.
If you move that only one of two not obviously wrong answers should be admissible, this qualifies not as proper but as parrot-learning. I do not want to commit to memory the treasure of sentencers here, I want to learn Danish!