The correct option is A Epidermis of human skin
Methanogens are microbes that belong to the domain Archae which include primitive forms of prokaryotes (organisms which do not have a well-developed nucleus). They are anaerobic archaebacteria that respire in the absence of oxygen and produce energy by the reduction of carbon dioxide into methane.
These organisms are extremophiles which prefer living in extreme conditions of temperature ranging from 4°C to 100°C and pH ranging from 3 to 9. Being strict anaerobes, they live in areas that have no oxygen exposure which would otherwise kill them. Thus, they prefer living in areas with extreme conditions such as marshes and bogs where water logging cuts of any oxygen supply. They cannot survive on the epidermis of the skin as it is the outermost layer of skin and has a lot of oxygen exposure.
They are also found in the rumen (first out of four stomachs in cattle) of cattle where they help in cellulose (a complex polymer found in plant cell walls) digestion. Cellulose in the stomach of cattle is broken down by certain decomposer microbes present in the rumen. The end products are finally acted upon by methanogens and in the process methane is produced.
Anaerobic sludge digesters are huge concrete tanks that are used to digest and break down the sludge (organic waste obtained from various industrial processes, sewage treatment, etc) by anaerobic bacteria in the absence of oxygen. This process yields biogas which is a gaseous mixture of carbon dioxide and methane and is used as a fuel for cooking and lighting. Thus methanogens are present in anaerobic sludge disgestors to help with biogas production.