What was the main impact of the Second Punic War on Rome in terms of territorial expansion?

The main impact of the Second Punic War on Rome in terms of territorial expansion is that it established Sicily as its first province. This event marked a significant moment in Roman history because it represented Rome's first formal engagement in imperial territorial governance. Following the First Punic War, Sicily became the first province under Roman control, setting a precedent for future provincial administration after the Second Punic War.

Through the conflicts with Carthage, particularly in Sicily, Rome solidified its territorial claims and gained experience in managing distant lands. The protection and governance methods developed for Sicily laid the groundwork for the Roman Empire's subsequent expansion into other territories. This administration proved crucial in facilitating Rome's growth into one of the ancient world's dominant powers.

The other choices represent different aspects of Roman expansion but don't capture the immediate significance of the Second Punic War as effectively. While Roman interest in Greece, alliances with other nations like Egypt, and eventual conquests of territories like Carthage did occur later, the establishment of Sicily as a province distinctly illustrates Rome's ambitions and transition toward major empire status during and immediately following the Second Punic War.