Question

Either you could retake the test tomorrow_____ you can do some extra credit

Answer 1

The correct option would be B. Or.
This is correct because whenever you see either, it will always be linked with or. 
Whenever you see Neither, it will always be linked with Nor.
Both C and D are not used to compare two things so they would be used alone.

Answer 2

The answer would be B. Or, because that would form the sentence "Either you could retake the test tomorrow or you can do some extra credit" which makes grammatical sense. I hope this helps!