How old was Nehemiah when he went to rebuild the walls of Jerusalem? It mentions that a Nehemiah left Babylon with Zerubbabel a long time before so is it the same Nehemiah?

ב"ה Shalom Your question has been troubling the commentators for generations. For as you said, it says in the book of Ezra 2:2 that Zerubavel and Nechemya were among those who returned from the exile of Bavel. According to Seder Olam chapter 29 and the Gemara in Megilla 11a, the return from the exile began 52 years after the destruction of the Bet Hamikdash. According to the pesukim, Zerubavel came to Eretz Yisrael the first year of the reign of Koresh=Cyrus, while Nechemia came to Eretz Yisrael in the 20th year of Artachshasta (Nechemia 5:14), but there is no mention of his age at the time. According to the Gemara in Sanhedrin 38a, Zerubavel and Nechemia are the same person, but Zerubavel is a contraction of two words in Hebrew "nizra b'bavel" meaning that he was raised in Bavel. So, if Zerubavel and Nechemia are the same person, how can the book of Ezra 2:2 enumerate them as two different people. One of the Rishonim, Meir ben Todros HaLevi Abulafia( Spain 1170- 1244) in the Yad Rema to Sanhedrin 37b says he is astounded at this Gemara, but offers no solution. Rav Chaim Benveniste (1603–1673) who was a prominent rabbinic authority in 17th century Turkey, offers the solution that the Nechemia mentioned in Ezra 2:2 is not Nechemia ben Chachalya but a different Nechemia. It should be noted, that the Rambam in his introduction to the Mishna, lists Nechemia and Zerubavel as two different people. The Chida, felt the version of the Rambam should be corrected so that the different names are to be understood as different names of the same person. (See Margaliyot Hayam Sanhendrin 38). Though you question, has been answered, this is a subject which deserves a more comprehensive article to address the issue. All the best