I think that Carroll’s use of the term “analysis” corresponds roughly to Barnard’s use of the term “understanding.” Carroll defines analysis* in a footnote (!) on page 13:
By analysis I am referring to the operation of explaining the ways in which the elements in the work function to realize the points or purposes of the work, or how they cohere as a unified whole, or the way in which they manage to embody whatever the work is about.
The key idea here is the notion of a holistic understanding of the work, that is, one’s unified big-picture understand of what the work fundamentally is about. So, in Reynold’s case, Gatsby is a quintessential American novel of modernity (his holistic understanding) and he uses descriptions, classification, contextualizations, etc., to construct (i.e., “analyze*”) and support that holistic understanding.