I am returning to school for another degree. The University does not accept the prior school college credits. I must submit an appeal so I do not have to repeat courses.

How do I write this appeal letter so that the courses from the prior school are credited to the new university?
You'll have to ask the university if they allow appeals against such decisions and, if so, how you need to go about appealing.
Check the university web site for credit transfers and appeals. For example, this is for the University of Washington:
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