- mind = håg (archaic in itself)
- to mind = ihåg
- remember = komma ihåg (literally "come to mind")
So we have a phrasal verb for remembering, i.e. one consisting of more than one word.
Now for the construction:
- The basic word order is du kommer ihåg mig (subject verb object)
- The question word order is (verb subject object) so you move the verb to the front: kommer ihåg du mig? (not grammatical - we're not done)
- But for phrasal verbs, you just move the first word to the front and leave the rest: kommer du ihåg mig?