Final answer:
Methane is primarily produced in the digestive systems of livestock and certain bacteria. Other sources include natural and anthropogenic activities, but in the context of the provided question, Option 2 is the correct source of methane production.
Step-by-step explanation:
Methane is produced in various settings, both naturally and through human activities. The most common source of methane, given the choices provided, is Option 2: in the digestive systems of livestock and certain bacteria. In the digestive tracts of ruminant animals such as cows and sheep, microbes decompose food in a process that generates methane as a by-product. Furthermore, certain bacteria in wetlands and other anaerobic environments can produce methane through a process known as methanogenesis.
While methane is also associated with fossil fuels such as natural gas and is a by-product of the combustion of hydrocarbons, the options pertaining to the exhaust systems of automobiles, coal-burning power plants, and home heating systems typically involve the combustion of hydrocarbons, where the main products are carbon dioxide and water, rather than the production of methane itself.