Complex sentence: The Cleveland family boss, Frank "Little Frank" Brancato, used Greene and other ethnic Irish gangsters to act as errand boys and muscle to enforce the Mafia's influence during the 1960s over the garbage-hauling contracts and other Mob-influenced rackets.
Split into simpler sentences: The Cleveland family boss, Frank "Little Frank" Brancato, brought in Greene and other gangsters of Irish heritage to act as errand boys and muscle to enforce the Mafia's influence during the 1960s. Greene was used as muscle in enforcing the Mob's control over the garbage hauling contracts and other Mob-influenced rackets.