The correct option is B sparsely
Option C: 'Sparsely' means 'in small numbers'. The words "you may not find a village for miles." confirms that there are hardly any people (consequently, villages) that can be seen in the hills. This refers to a sparse population.
Hence option C is correct.
Options A and B: 'Heavily' means 'in large amounts'; 'densely' means 'in a close or compacted manner'. Both these words describe a large population, a lot of people. But, the sentence states that there are hardly any villages, and hence, people in the area.
So, options A and B are incorrect.
Option D: 'Quietly' means 'in a quiet or silent manner'. It describes a quality, rather than the quantity (number). Hence option D is incorrect.