John Gill Commentary 2 Kings 14:1

"In the second year of Joash son of Joahaz king of Israel began Amaziah the son of Joash king of Judah to reign." — 2 Kings 14:1 (ASV)

In the second year of Joash son of Jehoahaz king of Israel
reigned Amaziah the son of Joash king of Judah .
] As Joash king of Israel began to reign in the thirty seventh of Joash king of Judah, (2 Kings 13:10) , reigned forty years, Amaziah must therefore begin his reign in the fourth of Joash king of Israel; this therefore must be understood of his second year after he reigned alone, for he reigned two or three years in his father's lifetime.