Source?
Josephus. Some Jewish traditions say 12. It is unclear if Solomon’s kingship started with his appointment by David, or is counted from David’s death. It is unclear how long David lived after Solomon’s appointment. Some scholars say two years, but could have been more.
There is no general agreement among scholars as to Solomon’s age when he became king, as his age was not recorded in the Bible.
However, Rehoboam, Solomon’s son, succeeded him as king at the age of 41 after Solomon’s death, which shows that Rehoboam was born when Solomon was 19 years old.
Solomon himself when speaking to God in his dream said:
1 Kings 3:7
And now, O Lord my God, thou hast made thy servant king instead of David my father: and I am but a little child: I know not how to go out or come in.