What is the name of the executive power they use to arrest somebody? As well as how does a legeslative power the power above and the original juirsdiction?

i think you are talking about the image i am uploading. then let's see who is who and based on that, let's answer your question about what section represents the state-level courts.

who is who:

box a: state trial courts box b: intermediate appellate courts   box c: state supreme courts box d: u.s. supreme court box e: u.s. courts of appeals box f: u.s district courts

which section represent state-level courts?

the correct answer is a, b, c.

box a or state trial courts are the bottom level and they decided about the 95% of the nation's legal cases.box b or intermediate appellate courts (also called state court of appeals in some states) are the second level above trial courts. they have the authority to review decisions and judgments of the trial court judges.box c or state supreme courts are the highest level in the u.s. state court system.   their primary responsibility consists of correcting the errors of the inferior state courts. they exclusively hears appeals on legal issues from inferior state courts. since state supreme courts do not make any finding of facts, they do not hold trials.