It is thought that Peter wrote his second letter around 60 - 62 AD. (1) The phrase "last days" is better translated in Young's as "the latter end of the days". Peter used a similar phrase in his first epistle.
"19 but with precious blood, as of a lamb unblemished and unspotted -- Christ's -- 20 foreknown, indeed, before the foundation of the world, and manifested in the last times because of you," (YLT)
This verse identifies when the last times were as Peter ties them to the days when Christ was manifested on earth. That means as Christ was manifested during the 1st century AD, the the last times, or last days happened during the 1st century AD.
As we are living today almost 2,000 years after Christ was manifested on earth, and time has continued on, then the phrase "the last days" cannot mean the end of all time. So, we must find in their definition in the scriptures, and there are specific instances the words are used in the Old Testament.
In Gen. 49, Jacob calls his sons to his deathbed to tell them what would happen to each of their tribes in their "latter days".
"And Jacob calleth unto his sons and saith, `Be gathered together, and I declare to you that which doth happen with you in the latter end of the days." (YLT)
The KJV uses "the last days." Jacob's reference to the latter end of the days was in context of the end of each of the tribes, and he proceeds to tell his sons how each of their tribes will end. The identification in time was the end of the tribe of Judah, the law giver, because Judah's end is tied to the passing of the scepter to Christ, in Judah's latter / last days.
"The sceptre shall not depart from Judah, nor a lawgiver from between his feet, until Shiloh come; and unto him shall the gathering of the people be." (KJV)
When did the scepter of the law giver pass from Judah to Christ? Legally, the scepter passed to Christ at His crucifixion in 30-31 AD, and officially probated at the destruction of the 2nd temple in Jerusalem in 70 AD when all of the Mosaic law was anulled (Heb. 7:18-19; 8:13).
So, the last days of Judah as described in Gen. 49 happened during the 1st century AD, and they were when the old Mosaic covenant passed away.
Daniel asked the messengers / angels twice when "these wonders" would end, and was told,
"...`After a time, times, and a half, and at the completion of the scattering of the power of the holy people, finished are all these.'" (Dan. 12:7, YLT) and the second time Daniel asked he was told,
"and from the time of the turning aside of the perpetual [sacrifice], and to the giving out of the desolating abomination, [are] days a thousand, two hundred, and ninety.'" (Dan. 12:11, YLT)
Therefore, "the end of the days" of Dan. 12:12 were defined as when the power of the holy people - Daniel's people, the Jews - would be scattered, or shattered, those wonders would be finished. And, when the perpetual or daily sacrifice was turned aside, or discontinued, then "the end" of those things would be finished.
When was the daily sacrifice at the temple in Jerusalem turned aside? Before or after that temple was destroyed? There can be no daily sacrifice at a temple that no longer exists. The turning away of that daily sacrifice was the start of the Roman-Jewish war in Jerusalem about AD 66-67. And, the power of the Jews / Sanhedrin over the people was shattered when their temple in Jerusalem was destroyed in AD 70.
So, again the last days, or the end of the days happened in the 1st century AD when the Mosaic sacrificial temple under the elements (2 Pet. 3:10) of the worship proscribed by the Mosaic covenant was destroyed. The "end of the days" of Daniel 12 is set in the context of the time given for the desolation of the Holy City - Jerusalem - in Dan. 9:24, the end of the 490 years of that prophesy.
Peter restates the prophesy from Joel 2:28 and refers to that prophesy as the "last days".
"15 For these are not drunken, as ye suppose, seeing it is but the third hour of the day. 16 But this is that which was spoken by the prophet Joel;
17 And it shall come to pass in the last days, saith God, I will pour out of my Spirit upon all flesh: and your sons and your daughters shall prophesy, and your young men shall see visions, and your old men shall dream dreams:
18 And on my servants and on my handmaidens I will pour out in those days of my Spirit; and they shall prophesy: 19 And I will shew wonders in heaven above, and signs in the earth beneath; blood, and fire, and vapour of smoke:
20 The sun shall be turned into darkness, and the moon into blood, before the great and notable day of the Lord come: 21 And it shall come to pass, that whosoever shall call on the name of the Lord shall be saved." (Acts 2:15-21, KJV)
"This is that..." Peter said that what the people saw and witnessed on the day of Pentecost was what Joel had prophesied would happen, and Peter restated the time as "in the last days." The pouring forth of the Holy Spirit upon the people on the day of Pentecost happened "in the last days", after Christ's crucifixion in the first century AD.
The "last days" spoken of in the Scriptures were never about the end of all time. The Scriptures define "the last days" as the time in which the old Mosaic covenant would pass away, and be fulfilled in Christ and His gospel of the new covenant, the everlasting covenant of His kingdom would be set in place. Those last days began when John came clearing the pathway and proclaiming that the kingdom was at hand, and ended when that animal sacrificial temple in Jerusalem was destroyed in AD 70.
- Dating the New Testament - here