Supporting details are facts, ideas and examples used to explain and develop the main ideas. Supporting details help us to understand key points.

What are some main questions, terms, and statements that relate back to the main topic? What are some supporting details, facts, and/or ideas that also help the overall argument of your paper?

The main clause or idea in this sentence is that Greg stayed behind, the reason or the supporting detail is that he had a detention, indicated by the subordinating conjunction 'because'.