Facility 4 is presumably the section of a cloning room that our heroes explore in "Shadow of Israphel" Part 40: Facility 4. The only known sections of the facility are a large rail system, a small cloning section where Professor Webley was found, and a small room where several details about the room can be found.
Honeydew and Xephos discover the room after trying to chase down Evil Honeydew. They find it underneath a giant robot buried beneath tons of sand. The facility was discovered after Evil Honeydew destroyed the minecart track that our heroes had been travelling across, blocking their path and stopping their chances of advancing.
It is believed to have been made by N-Comm, a mysterious organization that created many kinds of machinery in Minecraftia.