Prepositions are tricky.
You can accept your own answer in two days.
You can accept your own answer at the passing of two days.
The first sentence here is natural and common. The second is clumsy and strange, but it has the same meaning.
The preposition "in" typically refers to some sort of container. If I say "the gift is in a box", you understand that the box contains the gift. Regarding this ordinary usage, "in a box" and "within a box" mean pretty much the same thing.
When we use the preposition "in" with a period of time, we do not typically treat that period of time as a container. When we say things like "in a minute" or "in two days", we mean at that point in time at the end of the period. If I'm speaking literally and precisely, "I'll do it in a minute" usually means that first a minute will pass, and then I'll start to do it.*
In contrast, "I'll do it within a minute" does treat the period of time as a container. Here, whatever I'm doing is contained by the minute, and I should be done before that minute passes.
You can accept your own answer in two days.
You can accept your own answer within two days.
The two sentences above have completely different meanings. The fist refers to that point in time at the end of two days. The second refers to some point in time contained by those two days.
You can accept your own answer in two days.
You cannot accept your own answer within two days.
These two sentences have very similar meanings. In the first, accepting your own answer is possible at the end of the period. In the second, accepting your own answer is impossible inside the period.
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* Oddly enough, we often treat past-tense periods as containers, even with the preposition "in". "I did it in a minute" and "I did it within a minute" can mean the same thing. Prepositions are tricky.