Without seeing the paragraph or reading sample to which you refer, usually, the "general" details would follow the main idea sentence (typically the first sentence, but sometimes the second). General details will support your thesis statement. Specific details give support in the form of, for example only, figures, years, totals, sums, or other form of support. It may also involve a quotation. "Specific" details support the general details which support the main idea or thesis statement. Once a new point is introduced, which also supports the thesis statement or controlling idea, new specific information will tend to follow that up.
