Final answer:
The detail that best establishes the gothic setting in the excerpt is the haunting and dilapidated mansion where Dr. Jekyll resides.
Step-by-step explanation:
The detail that best establishes the gothic setting in the excerpt of The Strange Case of Dr. Jekyll and Mr. Hyde is 4) The haunting and dilapidated mansion where Dr. Jekyll resides. This detail paints a picture of a gloomy and eerie environment, typical of gothic settings. The dilapidated mansion adds a sense of decay and mystery, setting the stage for the dark and sinister events that unfold in the story.