Final answer:
The detail that shows Louisa is industrious is that she carefully collects the stems of currants, reflecting her diligent work ethic.
Step-by-step explanation:
The detail from the passage that best supports the idea that Louisa is industrious is: She sat on the back doorstep and stemmed them (currants), collecting the stems carefully in her apron, and afterward throwing them into the hen-coop. This exemplifies her diligent work ethic and attention to both productivity and neatness, which are hallmarks of being industrious. In contrast, the other details provided, such as being slow in movements, taking a long time to prepare tea, or being still while sewing, don't directly relate to the characteristic of industriousness.