It was a struggle for dominance of the Western Mediterranean.
The Romans persevered over Carthage .
By establishing a navy equal to Carthage's and developing superior tactics.
Carthage did not defeat Numidia. When she raised an army to defend herself, she was defeated by the Numidians. Then the Romans declared war and destroyed Carthage.
They defeated the armies of Carthage in the Punic Wars.
The defeat of the Carthaginian army by the Romans and their allies in front of Carthabe, with Carthage's capitulation.
Upon the defeat of Carthage the Romans won complete control of the western Mediterranean Sea.
Even after Carthage had been destroyed, people still thought of him with fear. A defeat like Cannae was not lightly forgotten.
It was a rival to Rome for domination of the Western Mediterranean.
In 149BC the Romans declared war on Carthage but the army was overall inefficient and unsuccessful in 147BC when Scipio Aemilianus is illegally elected consul. He whips the Roman army into shape and leads them to defeat Carthage in 146BC. Carthage was then destroyed.
The Romans destroyed Carthage in 146 BC.
They didn't want the city, they wanted to terminate it as a rival to control of the Western Mediterranean.
After the Second Punic War, a financial indemnity designed to cripple them for 50 years. They paid it back after 10 years.