Complex sentence: He played for the New York Yankees, Detroit Tigers, California Angels and Seattle Mariners all of the American League and the San Francisco Giants, Montreal Expos, Philadelphia Phillies and Milwaukee Brewers all of the National League.
Split into simpler sentences: He played for the New York Yankees, Detroit Tigers, California Angels and Seattle Mariners, all of the American League. He also played for the San Francisco Giants, Montreal Expos, Philadelphia Phillies and Milwaukee Brewers, all of the National League.