The two hog breeds mentioned in the crossword solutions are the Duroc and the Tamworth. The Duroc is a breed of domestic pig originating in the United States and is one of the oldest American breeds. It is a reddish-brown pig with drooping ears and a large, muscular body. The Tamworth is an English breed of pig that is reddish-brown in color and has long, straight snouts. It is known for its hardiness and is often used for bacon production. Both breeds are popular for their meat quality and are widely used in commercial pork production.