If you try to separate verse 23 from verse 22, what is the antecedent of the word "their" in verse 23?
Dan 8:22 Now that being broken, whereas four stood up for it, four kingdoms shall stand up out of the nation, but not in his power.
Dan 8:23 And in the latter time of their kingdom, when the transgressors are come to the full, a king of fierce countenance, and understanding dark sentences, shall stand up.
.
The first thing I notice is, the text says 'their kingdom', and not 'their kingdoms'. This can only mean the 4th kingdom, the one mentioned in Daniel 7, apparently. And besides, look what verse 8 and 9 say before we are given the interpretation in later verses.
Daniel 8:8 Therefore the he goat waxed very great: and when he was strong, the great horn was broken; and for it came up four notable ones toward the four winds of heaven.
9 And out of one of them came forth a little horn, which waxed exceeding great, toward the south, and toward the east, and toward the pleasant land.
This is apparently in regards to verse 22 and 23.
Daniel 8:22 Now that being broken, whereas four stood up for it, four kingdoms shall stand up out of the nation, but not in his power.
23 And in the latter time of their kingdom, when the transgressors are come to the full, a king of fierce countenance, and understanding dark sentences, shall stand up.
If we then go to Daniel 7---
Daniel 7:2 Daniel spake and said, I saw in my vision by night, and, behold, the four winds of the heaven strove upon the great sea.
3 And four great beasts came up from the sea, diverse one from another.
Notice that it mentions the four winds of the heaven. Also notice that it mentions the four winds of heaven in Daniel 8:8 as well. In Daniel 7:3 it involves 4 great beasts.
Daniel 7:17 These great beasts, which are four, are four kings, which shall arise out of the earth.
In this verse we see that beasts are kings. What do kings usually have? They have kingdoms.
Daniel 7:23 Thus he said, The fourth beast shall be the fourth kingdom upon earth, which shall be diverse from all kingdoms, and shall devour the whole earth, and shall tread it down, and break it in pieces.
This verse tends to prove that fact.
And in Daniel 8:22 it also mentions 4 kingdoms. then in verse 23 it mentions in the latter time of their kingdom, not kingdoms, when the transgressors are come to the full, a king of fierce countenance, and understanding dark sentences, shall stand up.
That has to be referring to the 4th kingdom mentioned in Daniel 7:23. And notice something else about this 4th kingdom.
Daniel 7:7 After this I saw in the night visions, and behold a fourth beast, dreadful and terrible, and strong exceedingly; and it had great iron teeth: it devoured and brake in pieces, and stamped the residue with the feet of it: and it was diverse from all the beasts that were before it; and it had ten horns.
8 I considered the horns, and, behold, there came up among them another little horn, before whom there were three of the first horns plucked up by the roots: and, behold, in this horn were eyes like the eyes of man, and a mouth speaking great things.
This little horn has to be the same little horn meant in Daniel 8:8, where we see in Daniel 8:23 that this is a king of fierce countenance, and understanding dark sentences, that shall stand up. This is also meaning the same one meant in Daniel 11:21 that stands up.