Step 1: Understand the context.
A miser is someone who hoards wealth and is reluctant to spend money. The sight of gold coins would excite and intensely attract him. Step 2: Match with suitable adverb.
- “Avidly” means with great interest or enthusiasm, matching the miser’s likely emotional state.
- “Admiringly” means with approval—possible but too mild.
- “Thoughtfully” means with consideration—does not match greed or desire.
- “Earnestly” means sincerely—again, less fitting here. Step 3: Final selection.
“Avidly” best captures the eagerness and greed in the miser’s gaze.
\[
\boxed{\text{(a) avidly}}
\]