Q: WHAT YEAR DID AHAZ BEGIN HIS REIGN IN JUDAH?
A: IT DEPENDS WHAT CALENDAR YOU ARE USING!
On the Gregorian calendar (the one you might have on your wall) the year was 676 BC.
On the Hebrew calendar, sometimes called the biblical calendar, the year was 3371 AM.
RELATED VERSES
2 Kings 15:32-33 New King James Version (NKJV)
Jotham Reigns in Judah
32 In the second year of Pekah the son of Remaliah, king of Israel, Jotham the son of Uzziah, king of Judah, began to reign. 33 He was twenty-five years old when he became king, and he reigned sixteen years in Jerusalem. His mother’s name was Jerusha the daughter of Zadok.
2 Kings 16:1-2 New King James Version (NKJV)
Ahaz Reigns in Judah
16 In the seventeenth year of Pekah the son of Remaliah, Ahaz the son of Jotham, king of Judah, began to reign. 2 Ahaz was twenty years old when he became king, and he reigned sixteen years in Jerusalem; and he did not do what was right in the sight of the Lord his God, as his father David had done.

3371AM/676BC