Cover beets with water. Boil until tender (about 25 minutes). Drain and cover with cool water. Set aside. Boil eggs in covered pan about 5 minutes. Remove from heat and let sit 15 min. This keeps egg yolks from having green color. Peel and set aside. In 1 qt. sauce pan, combine vinegar, onions and garlic. Bring to a boil. Remove and strain vinegar into a bowl. Return vinegar to pan reserving onions etc. seperately. In a jar place 4 eggs. After beets are cool enough to handle, peel and slice 1/4 inch thick. Place half of the beet slices over the 4 eggs, then half of the strained garlic and onion. Then layer again with remaining ingredients.