Is the italicized word in the sentence below an adverb or preposition? why don't you come over this evening (over)

The italicized word OVER can be used either as a preposition or as an adverb in a sentence. In this particular sentence, the correct answer is adverb.
When over is used as an adverb, it is not followed by any word which would create a phrase along with it (as is the case here). Compare OVER as a preposition (A bird flew over the lake - we can see over what) and OVER as an adverb (Could you come over - we don't know over where or what).