"Your car is next to my car."
Translation:Dein Auto ist neben meinem Auto.
neben is one of the group of prepositions that take the dative case to show location and the accusative case to show destination of movement.
Since the cars are just standing there, not moving anywhere, the dative case is used after neben.
That's why you have meinem Auto (dative case) rather than mein Auto (accusative case).
neben and an are both prepositions and can't both come before a noun -- just as you can't be, say, "before at the door" or "on by the table".
Perhaps you're thinking of nebenan (as a single word), but that's an adverb meaning "next door" -- it can't stand before a noun, just as you can't live "next door a factory", for example. ("next door TO a factory" yes, but not "next door a factory". And nebenan meinem Auto would be like "next door my car".)
Now, on the comments page, I see "Dein Auto" as a primary correct answer. Some time ago I've seen "Ihr", and someone seen "Euer".
Does correct answer change over time?
The sentence discussion pages show the translation that is marked as the best translation, rather than one of the additional alternatives.
But it's possible to mark multiple translations as "best" -- I think that the sentence discussion will then cycle through those.
In this case, the sentence marked "best" is "[Dein/Ihr/Euer] Auto ist neben meinem Auto." which stands for all three alternatives -- so you may see any of those three at the top of this discussion.
All of them are correct.
So meinem auto because you own the car or be cause it is being next to?
The -em ending in meinem is because of the preposition neben (next to), which requires the dative case when indicating a location. Auto is neuter, and -em is the appropriate ending here for neuter dative.