The question is a request to transform the optative sentence "Long live the King!" into a question (Interrogative).
Transformation of Sentences is the conversion of one "type" of sentence into another "type". The types are: assertive, interrogative, imperative, optative, and exclamatory. These categories, transformation rules, and examples are often found in ESL/EFL educational books.
The goal of transformation is a "very good" equivalence of meaning. How good is a "very good" equivalence? The only answer is "good enough" for whatever criteria is important. If taking a test, then "good enough" for the person grading the test. Beyond that, it's "good enough" for the needs of the writer/speaker.
How can a question "mean the same thing" as a statement? When one says,
"Will you please stop talking?" (Interrogative), they are not literally asking a question; they are politely saying,
"Stop Talking." (Imperative) or
"I want you to stop talking." (Assertive). Rhetorical statements like
"Is not wisdom better than riches?" (Interrogative) mean
"Wisdom is better than riches." (Assertive). Similarly, when one says
"Isn't this night beautiful?" (Interrogative), they mean
"This night is beautiful." (Assertive). Another form is the tag question,
"This night is beautiful, no?" (Interrogative).
"Long live the King!" is an "optative sentence": one that expresses a wish, desire, prayer, or hope. Optative sentences often start with "May" such as "May you live a long life." However, “Long live the King!” is an idiomatic expression that uses the subjunctive mood. In the subjunctive mood, the verb “live” is in the infinitive, e.g. to live, to be, to play, to run. Compare with third-person present tense, “The King lives long.”
This answer shows how to transform "Long live the King!" from optative to affirmative and then from affirmative to negative interrogative. (The OP updated that the teachers themselves could not answer this question and they discovered the textbook had a misprint! Such a double transformation is practically never asked in an ESL/EFL course. However, it can be done, and this answer is interesting because it's clearly within the ESL/EFL methodology to make each transformation separately.)
Subjunctive to Affirmative: First from subjunctive to various forms of a more affirmative style. Any of the following are equivalent meanings:
- Long Live the King! (Optative)
- May the King live long! (Optative)
- May the King live a long time! (Optative)
- May that the King lives a long time! (Optative)
- I wish the King to live long! (Assertive)
- I wish the King lives a long time! (Assertive)
- I wish for the King to live long! (Assertive)
- I wish for the King to live a long time! (Assertive)
- I wish for the new King that he lives a long time! (Assertive) *
- Let us all wish that the new King lives a long life! (Imperative) *
Affirmative to Negative Interrogative: Now from the affirmative to the rhetorical question, one uses a negation in this case. These are spoken (or written) in a context where the speaker's sentiment is obvious or conclusive. Any of the following could be a proper transformation of the original statement.
- Long Live the King, no? (This is a bit odd, but it works. It's more stylistic of Spanish and French.)
- Do we not all wish the King to live long?
- Who would not wish the new King to live long? *
- Who, amongst his loyal subjects, would not wish the new King to live long? *
- Who, amongst his loyal subjects, would not wish that the new King lives long? *
- Who's with me in wishing the King a long life? (Credit to @starsplusplus. Note this is "Interrogative" not "Negative Interrogative".) *
In my brief review of ESL/EFL prescriptions for transformations, there were a variety of "rules": some were rigidly syntactic while others allowed more semantic changes. There is no single "right answer" (other than a person grading your work). Consult with your instructor or exam requirements regarding "what is correct".
* The marked answers include variations that may push the boundaries of standard ESL/EFL transformations. What's the point of transformation if not to say the same thing in a different form?
Say "new King" if you need to make that idiomatic concept explicit. Similarly, "among his loyal subjects" may sound forced on its own, but it doesn't contradict the original meaning. All contextual meaning has to come from somewhere: an idiom, the environment/situation, prior sentences, character, or even from within the sentence itself.