This interpretation is not difficult. Isaiah is prophesying that before his son will be old enough to speak the kingdom of Syria (whose capital is Damascus) and the kingdom of Israel (whose capital is Samaria) will be taken by the Assyrians. This is a recurring theme from the preceding chapters. Isaiah could be referring to either the capture of the Israel and Syria described in 2 Kings 15:29 or the final destruction of Israel which occurred about ten years later, circa 722 BC, (2 Kings 17:6). The timing of these chapters suggests the former interpretation.
The external history of the Assyrians gives their version of the events described in 2 Kings 15:29. From the Cuneiform Text of Pul:
"His noblemen I impaled alive and displayed this exhibition to his land. All his gardens and fruit orchards I destroyed. I besieged and captured the native city of Reson [Rezin] of Damascus. 800 people with their belongings I led away. Towns in 16 districts of Damascus I laid waste like mounds after the flood.
"Bet-Omri [Israel] all of whose cities I had added to my territories on my former campaigns, and had left out only the city of Samaria. The whole of Nephtali I took for Assyria. I put my officials over them as governors. The land of Bet-Omri, all its people and their possessions I took away to Assyria.
"They overthrew Pekah their king and I made Hosea to be king of them." (Keller, The Bible as History, p. 245 as taken from Ludlow's Isaiah: Prophet, Seer, and Poet, p. 158).