Who compiled the Two Sahihs and the Six Books, and when was that done?

The compiler of these books is Majd al-Din Abu al-Sa'adat al-Mubarak Muhammad ibn Abd al-Karim ibn Abd al-Wahid al-Shaybani al-Jazari al-Mawsili, known as Ibn al-Athir, born in 544 AH. He was a jurist, a Hadith scholar, a man of letters, a grammarian, knowledgeable in arithmetic and composition, pious, wise, venerable, and charitable. His book is called "Jami' al-Usul fi Ahadith al-Rasul" (The Comprehensive Collection of Principles Regarding the Sayings of the Messenger). In it, he combined Bukhari, Muslim, Muwatta, Sunan Abi Dawud, Nasa'i, and Tirmidhi, arranging them alphabetically. He explained the obscure words of the Hadith, their meanings, rulings, and described their narrators. He passed away, may Allah have mercy on him, in 606 AH.