Option 1: Mollify -> means to soothe or calm someone's anger, not about satisfaction.
Option 2: Perpetuate -> means to make something continue indefinitely, unrelated to satisfaction.
Option 3: Gratify -> means to satisfy or please, similar to fulfilling a desire completely.
Option 4: Vanquish -> means to defeat thoroughly, not related to satisfaction.
Hence, Option 3: Gratify -> "Satiate" means to satisfy fully or fulfill completely, and "gratify" shares this meaning of providing satisfaction or pleasure -> correct