According to Arnold & Beyer, "Nahum mentioned the fall of Thebes, an event that occurred in 663 B.C. The prophet also speaks of Nineveh's fall, which took place in 612 B.C." (447). Due to this, we can conclude the dates of Nahum's ministry.
Nahum prophesized that Assyria's capital, Nineveh, would fall (Arnold & Beyer, 447).