Antipater was appointed regent of Macedon while Alexander the Great was away conquering the Persian Empire in Asia.
Alexander inherited a dangerous situation in Greece when he became king in 336 BC. Antipater, an experienced statesman who had served Alexander's father Philip II, remained in Macedon to govern the kingdom and supervise relations with the Greek states. He also commanded Macedonian forces in Europe, making him both the king's political deputy and a senior military leader.
During Alexander's absence, Antipater defeated the Spartan-led revolt known as the Lamian War after Alexander's death, but the appointment in this question refers to the earlier period of Alexander's Asian campaigns. Antipater's authority was not absolute: he had to manage Macedonian interests in Europe while Alexander's generals administered conquered territories in Asia.
The other options were important commanders, but they held different roles. Craterus served as a leading field commander, Parmenion was one of Alexander's senior generals, and Polyperchon became prominent later during the Wars of the Diadochi. Antipater eventually became regent of Alexander's empire after the settlement at Triparadisus in 321 BC.