When did Jehoiachin begin reigning and how long did he reign? II Kings 24:8 and II Chronicles 36:9 give two different numbers.
"Jehoiachin was eighteen years old when he became king, and he reigned in Jerusalem three months. His mother's name was Nehushta the daughter of Elnathan of Jerusalem" (II Kings 24:8).
"Jehoiachin was eight years old when he became king, and he reigned in Jerusalem three months and ten days. And he did evil in the sight of the LORD" (II Chronicles 36:9).
When dealing with dates we tend to be precise with small values and begin rounding as the value gets larger. We are likely to say that we moved into our new home three years ago, instead of noting that we moved into our new home three years, 2 months, 1 day, 5 hours, and 33 minutes ago. Therefore, for one account to say he ruled three months and another to say three months and ten days is simply a difference in what degree of rounding was done in the two records.
The starting date is most likely due to a copyist error. The difference between 18 and 8 is one letter. Two old translations, the Syrian and Arabic have 18 in both accounts. In addition, a few verses later we find that as Jehoiachin goes off into exile, his wives went with him (II Kings 24:15). This would make sense if he was 18 but is strange if he was only 8.
Another possible explanation is that many kings trained their successors. David did this with Solomon to prevent contentions over who would succeed him to the throne, and it became a common practice among his heirs. It is possible that Jehoiachin began a co-regency with his father, starting at the age of eight, and became the sole king at the age of 18. However, eight would be an unusually young age to start a co-regency, so I don't think this possibility is quite as likely.
A final possibility comes from when you start counting years. In I Samuel 13:1 the literal Hebrew sounds like Saul started reigning when he was one year old, but likely what is being stated is that the event occurred in the first year of his reign (See "When did Saul rule Israel?"). It just sounds odd to Americans because we don't speak of time in that manner. Jehoiachin's father Jehoiakim reigned for 11 years (II Kings 23:36). In the fourth year of his reign, the Babylonian captivity began (Jeremiah 25:1) when Jehoiachin was 10 years old. Thus, it is possible to say that Jehoiachin was both 18 (from his birth) and 8 (from the captivity) at the same time.