In a large 4 to 5 quart saucepan, heat olive oil over medium heat. Mix in garlic, onion and carrots. Saute the vegetables until just tender; approximately 5 minutes.
Add tomatoes with juice, cannellini beans, and kidney beans to the saucepan. Fill each can with water, and add the water to the saucepan. Mix in green beans and zucchini. Sprinkle parsley, basil, oregano, Italian seasoning, bay leaves, chicken-style seasoning, and cayenne pepper into the soup; stir well. Bring the soup to a boil, then reduce heat to simmer. Cover, and let simmer 30 minutes.