What are three books that are burned at the old woman's house, and three books that are burned at Montag's house?
The answer to the first portion comes when Montag is attempting to talk to Mildred later that night. Of course, she's only interested in her "programmes", and when Montag pukes on the floor she gets very upset. He tries to tell her about the old woman, choosing to die with her books, but she doesn't get it. He tells her: "We burned copies of Dante and Swift and Marcus Aurelius." So most likely, they burned Dante's The Divine Comedy, known commonly as Dante's Inferno. They burned books by Jonathan Swift, most likely Gulliver's Travels. They also destroyed the writings of Marcus Aurelius' Meditations, written while he was Emperor of Rome.
As far as those books burned at Montag's house, these are more difficult to pin down. The only one that's directly named is the Bible. Montag shows his wife, saying "This is the Old and New Testaments". Later on, Montag becomes the books of Ecclesiastes and Revelation. So the Bible is definitely one. A second book is most likely an anthology of poems, because Montag reads "Dover Beach" to Mildred's friends. but no title is given, and that's the only poem read from it. The others are a mystery. At least one may be some kind of pulp fiction, because it has an ad for "Denham's dentrifice" in it. Otherwise, we'll never know what's burned in his house.