How to determine the state and federal functions and jurisdiction of a case?

I have some questions I have to answer for my homework and the text only explains a portion of the answers. In the assignment we are to review 5 cases then determine if each of the cases is a function of a federal or state court if the case falls under federal or state jurisdiction. My question is what elements of the case determine the function and the jurisdiction as they are not explained in the text. The five cases are a drug case The SUpreme court of the State v. a private citizen, a domestic violence case also the Supreme court of the state V. a private citizen, A sexual Battery appellant case United States V. Private citizen, a dispute over double jeopardy where it was citizen v. state. I am having difficulty getting the last one to open so i dont know what it is about. Any help would be very much appreciated.