We cannot read NT passages into the Old Testament to explain difficulties - each passage must be understood in its own context. Otherwise I would read the second half of 2 Pet 3:8 into Genesis and say that Methuselah was almost a day old when he died. Instead, I'll give an OT example with similar wording to try to understand the meaning behind the Hebrew language better.
The following verses are excerpts from the story in 1Kings 2:36-46, where Solomon tells Shemei to stay in Jerusalem and later executes him for disobeying. In this story, Shemei travels from Jerusalem to Gath and back, a journey of at least two days - he probably spent a few days in Gath as well.
1 Ki 2:37 For it shall be, on the day you go out and cross the Brook Kidron, know for certain you shall surely die; your blood shall be on your own head.”
1 Ki 2:42-43 Then the king sent and called for Shimei, and said to him, “Did I not make you swear by the Lord, and warn you, saying, ‘Know for certain that on the day you go out and travel anywhere, you shall surely die’? And you said to me, ‘The word I have heard is good.’ Why then have you not kept the oath of the Lord and the commandment that I gave you?”
So Solomon, at least a few days after Shemei's disobedience, still does not consider his threat that "on the day" Shemei disobeyed, he would surely die.
Though Shemei was not physically executed on the day he disobeyed, nor did he die spiritually on that day, on that day his physical death became certain. In English terms, we might literally say, "on the day he left Jerusalem, he was as good as dead."
It is possible that Genesis is making a similar point - not that Adam died physically on that day, nor that he died spiritually that day (indeed, how could God threaten beings who do not "know good and evil" with spiritual death and expect them to understand?), but that his physical death became certain the moment he disobeyed.