Final answer:
The Carthaginians held off the Romans for over a century across the three Punic Wars, spanning from 264 BCE until their final defeat in 146 BCE.
Step-by-step explanation:
The conflict between Rome and Carthage, known as the Punic Wars, spanned over a century and involved several phases of warfare. The First Punic War began in 264 BCE, ignited by disputes over the island of Sicily. Despite initial Carthaginian naval superiority, Rome's relentless pursuit of victory and innovative naval tactics eventually led to Carthage seeking peace in 241 BCE, thus holding off the Romans for 23 years during this first confrontation.
Peace between the two powers was short-lived, as Carthage, led by the great general Hannibal during the Second Punic War (218-201 BCE), sought revenge. Hannibal's legendary campaign, including his crossing of the Alps and victories at Trebia, Lake Trasimene, and Cannae, terrorized Rome but did not result in a definitive Carthaginian triumph. The stalemate persisted until Roman General Scipio's counter-invasion of North Africa forced Hannibal's return, concluding the war with Rome's favor.
Finally, the Third Punic War (149-146 BCE), prodded by enduring Roman enmity towards Carthage and persistent fears of Carthaginian resurgence, was significantly shorter and ended with a Roman victory marked by the brutal sack of Carthage in 146 BCE. In total, Carthage managed to hold off Roman domination until their final defeat, meaning they resisted for over a century, from 264 BCE to 146 BCE amidst intermittent warfare and uneasy peace.