Di Goyim always have a hard time remembering how many days is in each month. This is because, for some reason, February has only 28 days, so instead of simply alternating 31-29-31-30-31-30-31-30-31-30-31-30, with February having 30 days on leap years, it has to go 31-28-31-30-31-30-31-31-30-31-30-31.
The Hebrew calendar (best calendar) doesn't have this problem! Months always go 30-29-30-29-30-29-30-29-30-29-30-29 (regardless of whether you consider Nisan or Tishrei to be the first month.) It alternates! No need to memorize anything. Last month had 29 days? This month has 30 days. (Unless it's a leap year1)
Unless, obviously, Yom Kippur would fall on Shabbat or the day before Shabbat (preventing us from adequately preparing for Shabbat), that is to say, on a Friday or Saturday. We also can't allow Hoshanah Rabbah2—the seventh day of Sukkot—to fall on Shabbat, because we need to carry willows for Hoshanah Rabbah and that would be a violation of Shabbat.
So to prevent either scenario, Rosh Hashanah can only occur on a Monday, Tuesday, Thursday, or Saturday; so if R"H was going to occur on a Wednesday, Saturday, or Sunday, we need to delay it! Sometimes, due to math, we might even need to delay it multiple days. But by delaying R"H, that causes the previous year to run long, and the following year to run short. In fact, this process, in addition to how the Hebrew calendar handles leap years1, means Hebrew years can have six different possible lengths. 353. 354, 355, 383, 384, or even 385 days!
Regardless, the Gregorian month that the English call "November" tends to overlap with the normal months of Cheshvan and Kislev. So if you need to adjust for delaying Rosh Hashanah, you can add or subtract days from Cheshvan and/or Kislev.
So sometimes it's 30-29-30-29-30-29-30-29-30-29-30-29, but sometimes it's 30-29-30-29-30-29-30-30-30-29-30-29 (or 30-30-30-29-30-29-30-29-30-29-30-29, if you consider Tishrei the first month); and sometimes it's 30-29-30-29-30-29-30-29-29-29-30-29 (or 30-29-29-29-30-29-30-29-30-29-30-29 if you consider Tishrei the first month); and I'm not sure if this ever happens given math and astronomy but according to halakhah it is permissible to also have 30-29-30-29-30-29-30-30-29-29-30-29 (or 30-30-29-29-30-29-30-29-30-29-30-29)3
This is easily memorable with the simple mnemonic
Thirty days have Tishrei, Nisan, Sivan, Shevat, Av, and sometimes Kislev and Cheshvan. All the rest have 29, except sometimes Kislev and Cheshvan.
But hey, most of the time it's pretty easy to remember, right?
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Maimonides found a passage implying years should be counted by months, not by days, so we can't have a "leap week" it has to be a "leap month" so we wait for a month's worth of missing days to accrue and then repeat the entire month of Adar twice in one year. So I guess "if the last month had 29 days, this month has 30 days" doesn't apply if the last month and the current month are the same month. Adar II is still Adar, of course, so of course it would still be 29 days both times, it's the same month! Of course the same month would have the same length.
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In the diaspora, many Ashkenazi Jews actually perform Hoshanah Rabbah right at twilight at the end of the seventh day of Sukkot so that it flows into Shemini Atzeret/Simchat Torah, so you might not even realize these are two different consecutive holidays.
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During a leap year, you can also have 30-29-30-29-30-29-30-29-30-29-30-29-29, 30-29-30-29-30-29-30-30-30-29-30-29-29/30-30-30-29-30-29-30-29-30-29-30-29-29, 30-29-30-29-30-29-30-29-29-29-30-29-29/30-29-29-29-30-29-30-29-30-29-30-29-29, or 30-29-30-29-30-29-30-30-29-29-30-29-29/30-30-29-29-30-29-30-29-30-29-30-29-29.