This exercise says that it should be अगले दिन whereas the exercise linked below requires अगला दिन:
This seems inconsistent to me, but I may be misunderstanding. Can anyone explain if one is incorrect and, if not, what determines अगला vs अगले?
Think of this one as "ON the next day." There is an assumed pre/post-position (e.g. on, in, at , during) there in the deep structure of grammar even if it is going unsaid. The presence of this postposition puts the phrase "next-day" into the oblique case.