'Day' as a preposition [closed]
Solution 1:
In your sentence, the next day is an adjunct of temporal location which is realized by a noun phrase (NP).
True, adjuncts of temporal location are very often realized by preposition phrases (PPs), but certainly not always.
In your sentence, either a PP or an NP would work, but that is not always so. Consider, for example,
[1] Last night, I came home late.
Here last night is also an NP. But in this case, there is no preposition that can be attached to it to convert it to a PP such that the meaning remains the same.