Though I have looked at several feasible explanations to this challenge, I have never read or studied out any answer that totally convinced me that it was the correct one. Personally, I believe God left this as a test of our faith in His preservation of every jot and tittle of His word.
You see, this is not a problem with the King James translation. The King James translation of 2 Chronicles 22:2 with Ahaziah being 42 years old is the correct translation of every extant Hebrew manuscript of 2 Chronicles. Even the NIV has a footnote stating that the Hebrew says forty-two in this passage. The King James translation is honest and correct. Those who change it to 22 are trying to help God out; they are interpreting and not translating at all.
The question is how this obvious "error" could remain in the Hebrew texts of the Old Testament. This is especially pertinent since Jesus promised, "Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled" (Matthew 5:18). I suppose you could say that the "law" is confined to the five books of Moses, but the word is often used of the entire Old Testament corpus. The personal question is whether we are going to believe Jesus or the critics. I have a strong propensity for believing God first and last and I choose to do so with these verses.
As to some form of reconciliation of the readings, we need to know that something weird is going on in the time dealt with in these verses. Ahaziah is the king of Judah, but his mother is Athaliah the daughter of Omri the king of Israel. Also, Athaliah had a brother named Ahaziah who had been king of Israel before he died. This time period sees intermarriage and intermingling between the royal lines of Israel and Judah. There are not only two Ahaziah's; there are also two Jehoram's (or Joram's) and two Jehoash's (or Joash's)--always one each from each kingdom. There is a plot and attempt to destroy the royal line of David. And, there is much joining of the two lines. There is more, but I will not take the time to give other details at this time.
As to Ahaziah being both 22 and 42 at his coronation, there are several possibilities. One age could be biological and the other could be assumed (in the name of someone else). For instance, he could be 22 biologically (fitting with the age of his father) and could also have assumed the age of his uncle Ahaziah (who had been king of Israel) in an attempt to bring the two kingdoms together. This would certainly fit the later actions of Athaliah in killing the seed royal and taking over the throne of Judah.
Another possibility is that he had been coronated twice but did not actually take the throne until he was 42. This would make him older than his father, but that would be possible if he were adopted for the purpose of placing him in the royal line. This kind of thing was done in the Roman succession many times. I have heard other possibilities as well.
But, the truth is, I have never seen the clincher in scripture that settles the thing once and for all. I do not know which possibility is the actuality. But this should be no hindrance to accepting it as truth. If one goes from where I am across town, I know of several ways they could go. There are even ways that I probably would never think of. But if someone tells me they left my place and ended up across town, my ignorance of the path they took does not mean that there was no way for them to get there. I can believe them without knowing the path they took.
What you and others have to decide is whether God did or did not preserve His words in the Hebrew Old Testament. This is not even a question of translation. Is the jot and tittle stuff a bunch of junk or is it the word of God? That is the question. For me, it is an easy choice. God promised to preserve His word and I believe He did. For others, it may be more complicated.