How did the Nazis manage to cremate 6 million Jews, along with many thousands Roma (gypsies) etc?

Not all 6 million were gassed and cremated. To carry-out state-sponsored genocide took the complicity and involvement of all walks of German life, from the Gestapo that rounded up the Jews in the occupied territories to the trainmen that hauled the loads to the death camps...to the contractors who built the crematia and gas ovens...to the pharmaceutical conglomerate that provided the Z-clone B. By the summer of 1944, IG Farben was providing 4 1/2 tons of Z-clone B to the SS per their bills of lading produced by the prosecutors at the Nuremburg trials after the war.

In 1942, the six Auschwitz ovens could have consumed about 4500 per month. The highest monthly death total for registered prisoners at Auschwitz was 9000 in September 1942. By the summer of 1944, an additional 12 ovens were constructed with a capacity of 420 bodies per day or about 12,500 per month. The Nazi records indicate they topped out 26,000 per day during the summer of '44. The crematoria were ordered destroyed by Himmler in Nov. of '44 as the Red Army approached from the East. Some good web sites on the subject:

http://remember.org/eichmann/timeline.htm

Books on WWII