Left Panel
I don't know how to eliminate all the choices, but the answer for this question is E.
A is incorrect. Out of 10000 cases making an appeal to the Supreme court, only 80 are hear.
B: Sometimes a case is heard if only 1 justice wants to hear it because the case is in the realm of his specialty. So B is not true.
C: C is one of those possibilities that is possible that might be true. Actually the cases presented to the court go through a pool of clerks who decide whether or not to pass it on.
D: For the same reason that B is not the answer, I don't think this one is either. The court has in recent history had an odd number of justices. I don't think the chief justice has any more votes than any of the others. The vote rarely is 4 to 4 close, especially recently.
Middle Panel
The answer to this is D to make and pass laws that apply to the state. I'll explain this better in the comments when I'm at home.
Right Panel
I think the closest answer is A. I'll put this one in the comments as well.