“In the days of Ahaz” means about 735 b.c. onward. The nations, capitals, and rulers involved are as follows:
Nation (alternate name)  | Capital  | Ruler  | 
Judah  | Jerusalem  | Ahaz  | 
Israel (Ephraim)  | Samaria  | Pekah, son of Remaliah  | 
Syria (Aram)  | Damascus  | Rezin  | 
See these place-names on Maps 9 and 10 in the Latter-day Saint edition of the King James Version of the Bible.
Syria and Israel had formed a coalition to block the armies of the Assyrian Tiglath-pileser III as they advanced westward. Ahaz, king of Judah, refused to join. Syria and Israel then decided to march on Jerusalem and replace Ahaz with a man of their own persuasion. Verse 2 says King Ahaz’s “heart was moved” or shaken.