She _________ that she _________ the assignment in a month from today.

Concept: When the reporting verb is in the past tense ("said"), the verb inside the reported clause usually backshifts one tense (for example, "will" becomes "would"). This backshift is not required, however, when the time of the reported action is tied to the present moment (words like "today," "now," or "this week") rather than to the past moment of speaking - the action is still genuinely ahead of us relative to now, so its tense is kept as it was.

Application: In this sentence, the reporting action already took place, so the first verb must be past tense ("said," not "says"). The second verb describes something due "in a month from today" - anchored to today, not to the past moment of speaking - so it stays future in form as "will finish" rather than shifting to "would finish." A bare gerund such as "finishing" cannot fill this role at all, since the clause needs a fully finite verb.

Cross-check: If the phrase had instead read "a month from then" (measured from the moment of speaking), backshifting to "would finish" would be required. Because the sentence explicitly anchors the deadline to "today," the future tense is preserved instead.

Why the other choices do not work:

• A present-tense reporting verb paired with a bare gerund does not fit a narration of something already said, and a gerund alone cannot be the clause's finite verb.

• The reporting verb is right, but a bare gerund still cannot serve as the finite verb the clause needs.

• This holds only if no listed option forms a complete, grammatically valid sentence; one of them does.

So the sentence reads: "She said that she will finish the assignment in a month from today."