The holiday of Shemini Atzeret/Simchat Torah, falls on the Hebrew calendar dates of 22-23 Tishrei—Shemini Atzeret on the former date, Simchat Torah on the latter. Here are the coinciding secular dates for the upcoming years:
2016: October 23 (at sundown)-25
2017: October 11 (at sundown)-13
2018: September 30 (at sundown)-October 2
2019: October 20 (at sundown)-22
2020: October 9 (at sundown)-11
Note: The Jewish calendar date begins at sundown of the night beforehand. Thus all holiday observances begin at sundown on the secular dates listed, with the following day being the first full day of the holiday. Jewish calendar dates conclude at nightfall.