Thus, in less than twenty years, Rome had destroyed the power of one of the successor states, crippled another, and firmly entrenched its influence over Greece. This was primarily a result of the over-ambition of the Macedonian kings, and their unintended provocation of Rome; though Rome was quick to exploit the situation. In another twenty years, the Macedonian kingdom was no more. Seeking to re-assert Macedonian power and Greek independence, Philip V's son Perseus incurred the wrath of the Romans, resulting in the Third Macedonian War (171–168 BC). Victorious, the Romans abolished the Macedonian kingdom, replacing it with four puppet republics; these lasted a further twenty years before Macedon was formally annexed as a Roman province (146 BC) after yet another rebellion under Andriscus. Rome now demanded that the Achaean League, the last stronghold of Greek independence, be dissolved. The Achaeans refused and declared war on Rome. Most of the Greek cities rallied to the Achaeans' side, even slaves were freed to fight for Greek independence. The Roman consul Lucius Mummius advanced from Macedonia and defeated the Greeks at Corinth, which was razed to the ground. In 146 BC, the Greek peninsula, though not the islands, became a Roman protectorate. Roman taxes were imposed, except in Athens and Sparta, and all the cities had to accept rule by Rome's local allies.

Answer this question, if possible (if impossible, reply "unanswerable"): When did the Greek peninsula become a Roman protectorate?
146 BC