Final answer:
The narrator's respect for her father's response to challenges is best illustrated by the comparison to a steadfast marble statue, symbolizing strength and resilience.
Step-by-step explanation:
The detail from the passage that best supports the idea that the narrator respects how her father responds to challenges is "Dad stood strong and still, like a marble statue of a soldier I remembered seeing at a park." (paragraph 11). This simile suggests a comparison between the father's demeanor and a steadfast statue, which often symbolizes resilience and strength. The narrator's respect is conveyed through the admiration implicit in the comparison to such a symbol of steadfastness in the face of difficulty.