The 4th of Ab, 455 B.C.E.
Interestingly, earlier in this same Insight volume, it mentions that the 20th year may not have started until Tishri (September/October) by Nehemiah's reckoning:
The month of Chislev (November-December) of a certain 20th year is the reference point with which the historical narrative begins. (Ne 1:1) As is evident from Nehemiah 2:1, this 20th year must be that of Artaxerxes’ reign. Obviously, the 20th year in this case is not reckoned as starting in Nisan (March-April), for Chislev of the 20th year could not then precede Nisan (mentioned at Ne 2:1) of the same 20th year. So it may be that Nehemiah used his own count of time, reckoning the lunar year as beginning with Tishri (September-October), which month Jews today recognize as the beginning of their civil year. Another possibility is that the reign of the king was reckoned from the actual date that the monarch ascended the throne. This could be so even though the Babylonian scribes continued to reckon the years of the Persian king’s reign on their customary basis of a Nisan-to-Nisan count, as their cuneiform tablets show they did. it-2 p. 487-488
But, to answer your question, Ab 4, 455 B.C.E.