The most appropriate layering process for a compost pile from the given options is:
a layer of grass clippings, a layer of fruit scraps, some soil, and some water.
This option includes green materials (grass clippings and fruit scraps) that provide nitrogen, along with soil to introduce microorganisms, and water to maintain moisture, which is essential for the composting process. The other options are not ideal due to inappropriate materials (like paper napkins and cheese) or poor layering combinations.