"Does Péter love me or you?"
Translation:Péter engem szeret vagy téged?
The Hungarian word order?
Hungarian sentences are usually constructed as topic-focus-verb-rest.
Péter is the topic in this sentence. The sentence is about him. He also doesn't have any suffix or postposition attached to his name, so we know that he's the subject here, doin' the lovin'.
Engem is in the focus. Why are we putting it in the focus? Because we want to compare it with téged. Does he love me or does he love you? Engem and téged are the direct-object forms of én and te, respectively.
Szeret is the verb, the heart of the sentence. The verb gets conjugated according to the subject - in this case in the (suffix-free) 3rd-person singular form.
So, you could translate this sentence in a bit more expressive way, making clear what topic and focus is: "Regarding Péter, is it me whom he loves, or is it you?"
Jere, Hungarian generally doesn't bother with 'S' and 'O', but it rather aims for a T-F-V order: topic-focus-verb.
In this sentence our focus is on "us" - does Peter love me or does he love you. That's the important part of the sentence and as such it has to be placed in front of the verb: "Engem szeret vagy téged?" or "Engem vagy téged szeret?"