Final answer:
Surface mining, especially mountaintop mining, is the most environmentally damaging extraction method due to the destruction of natural habitats, ecosystems, and the landscape, alongside water contamination and increased erosion.
Step-by-step explanation:
Among the methods of extraction listed, surface mining, particularly in the form of mountaintop mining (MTM), is considered to be the most damaging to the environment. MTM involves removing mountaintops to expose coal seams, which not only destroys the natural habitat and landscape but also has severe consequences such as burying streams with the displacement of debris. This practice leads to the destruction of ecosystems, contamination of water sources, and increased erosion, making it a significant environmental concern. While other methods like subsurface mining, placer mining, and processes like fracking have their own negative environmental impacts, MTM stands out for the scale and permanence of the damage it causes to the earth's surface and ecosystems.