The original sentence uses present tense for the if clause, and "will" for the main clause. In the common classification of conditional sentences, this is an example of the first conditional, which is what we use when we talk about real and possible situations.
Looking at the three possible answers:
"She said if I did not do it by Friday I would be punished" - the if clause is in the past tense, and the main clause uses "would". This becomes a second conditional, which is used to talk about unreal or impossible things. In this case, it likely means that Friday is already past, and you cannot change the fact of "doing it" (or "not doing it"). This is a grammatically correct sentence, and it reports a saying in the past about a condition that is also in the past.
"She said if I do not do it by Friday I would be punished" - the if clause is in the present while the main clause uses "would". This does not match the classical conditional sentence structures. There is a "mixed conditional" structure that some people may associate with this sentence, but as described here its common uses are different; it is not typical to mix first and second conditionals.
(Note that if you want to report a saying in the past about the future, you should use "She said if I do not do it by Friday I will be punished". This is a reported version of the first conditional; Friday is now in the future and you can still "do it". This could be a correct answer to the question, but it is not one of the suggested options...)
"She said if I would not do it by Friday I would be punished" - here the if clause uses "would". This does not match any of the conditional structures. Using "will" or "would" in the "if" clause is definitely wrong English (although you may hear it often).
If you need to choose one of these options, the first one is likely the correct answer.