The 6 1/2 hours comes from the sacrifice of the tamid which started at 12:30 PM called mincha gedaloh and sacrificed at 9 1/2 hours or 3:30 called called mincha ketana. According to the Rabenu Taam we we can daven mincha until his ben hashmoshos 58 1/2 min after the first shkiah when night starts.
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