The most appropriate layering process for a compost pile among the options provided is:
a layer of grass clippings, a layer of fruit scraps, some soil, and some water.
This combination includes a good balance of green materials (grass clippings and fruit scraps, which provide nitrogen) and brown materials (the soil, which adds carbon, and the moisture necessary for decomposition). The other options either include materials that are not suitable for composting (like cheese) or lack a proper balance of greens and browns.