During which famous war was Carthage burned to the ground by the Roman Empire?

The correct answer is - the Third Punic War.

The Punic Wars were a series of three wars between the Roman Empire and the Phoenician colony of Carthage. They took place in a span of 82 years, from 264 BC to 146 BC. In the last of the three wars, the Third Punic War, the Romans managed to defeat Carthage and they burned it to the ground, and that marked the end of the Phoenician influence in the Mediterranean region.

The name of the wars, Punic, comes from the Latin Punicus/Poenicus, which actually means Phoenicians, and is referring to the ancestry of the Carthaginians.