Final answer:
H.M. improved in the mirror tracing task over time due to intact basal ganglia, allowing for the formation of procedural memories despite his anterograde amnesia.
Step-by-step explanation:
The best explanation for why H.M. showed improvement at the mirror tracing task across days/weeks is that his surgery did not impact his basal ganglia. Despite H.M.'s inability to form new episodic or semantic memories due to his anterograde amnesia from the bilateral removal of his hippocampus and amygdala, he was able to form new procedural memories. The basal ganglia, which were intact in H.M., are involved in the development of procedural memory, allowing him to improve in tasks like mirror tracing without conscious recollection of having learned the task.