The correct option is A Avidly
Option A: 'Avidly' means 'with great interest and enthusiasm'.
Option B: 'Admiringly' means 'in a way that shows respect or warm approval'.
Option C: 'Thoughtfully' means 'in a way that one is absorbed in thought'.
Option D: 'Earnestly means seriously.
As per the context of the sentence, the word 'avidly' is most suitable as enthusiasm goes with the words "miser... pile of gold coins". Hence A is correct.
The other words do not complete the meaning of the sentence. The thought 'a miser looking at a pile of gold coins with respect, thought or sincerely' doesn't put the meaning through as it does with 'enthusiasm'.
Hence B, C and D are incorrect.