Matthew’s genealogy is edited, and by that I mean he has omitted certain kings in the second section (Matt 1:6b-11). Here are his fourteen generations represented by names: Solomon, Rehoboam, Abijah, Asaph, Jehoshaphat, Joram, Uzziah, Jotham, Ahaz, Hezekiah, Manasseh, Amos, Josiah, and Jechoniah.
In 2 Kings, it is clear that between the reigns of Joram and Uzziah are three other kings: Ahaziah (2 Kgs 8:25-29), Jehoash (2 Kgs 12:1-21), and Amaziah (2 Kgs 14:1-22). Matthew condenses the genealogy by omitting these three rulers. This is not historical ignorance or oversight. Matthew explains in 1:17 that he has a numerical design to the genealogy of 1:2-16. And since he wants to show fourteen generations, some kings have to be left out. Ahaziah, Jehoash, and Amaziah were all evil kings, so we’re not missing anything edifying. They were a trinity to ignore!
Then between Josiah and Jechoniah (aka Jehoiachin), Matthew omits Jehoahaz (2 Kgs 23:31-34) and Jehoiakim (2 Kgs 24:1-2). Again the reason appears to be his literary design.
The last reigning king in the Davidic line before the exile was not Jechoniah, however. It was Zedekiah, Jechoniah’s uncle. Zedekiah, then, is another Matthean omission. Why leave out the last king of Judah? Grant Osborne is probably right: Matthew believed the Babylonian exile began under Jechoniah’s reign and so focused on him (Matthew, ZECNT, 66-67).
In summary, what were the omissions Matthew made in the second section of his genealogy (Matt 1:6b-11)?
Had Matthew included all these names, the generations would have numbered twenty instead of fourteen. Fourteen, for Matthew’s purposes, was very important (cf. Matt 1:17).