The rule with “Neither…nor” is that the verb agrees with the subject closer to it.
In this case, “his ministers” is plural and is closer to the verb, so the verb must be plural — “desire,” not “desires.”
Option (A) and (B) incorrectly use the singular verb “desires,” which would match only if the closer subject were singular.
Option (D) has correct verb agreement but omits the definite article “the” before “king,” making it incomplete and less formal.
Option (C) is correct because it uses the definite article “the” before “king,” keeps “his ministers” in plural form, and uses the correct plural verb “desire” in agreement with the nearer subject.