Question: "Why do you say that Cheshvan is the eighth month of the Jewish calendar? Isn't it the second month?"
Great question! From this answer you will understand why so many Jews are accountants or bookkeepers .
The Talmud, in Tractate Rosh Hashana, says the following: "There are four new years*. The first of Nissan is the New Year for kings and for festivals... On the first of Tishrei is New Year for years."
In other words, Nissan is the first month for counting the months. How do we know this? Torah says, "This month shall be to you beginning of months. It shall be the first month of the year to you." (Exodus 12:2) This is said in reference to the month of the Exodus, the month of Pesach, which is also the month of spring.
There are many quotes in Tanach that support this and count the months based on Nissan being the first month. For example, "And Esther was taken to King Achashverosh, into his royal house, in the tenth month, which is the month of Teves." (Esther, Chapter 2) In this counting Cheshvan is the eighth month.
Tishrei is the first month for counting the years. Adam was created on the first day of Tishrei, therefore we count years from then.
"In the 600th year of Noach's life, in the second month, on the 17th day of the month, on this day all the spirngs of the great deep were split, and the windows of the heavens opened up."
Rashi comments on this verse: "Rabbi Eliezer says this refers to Marcheshvan; Rabbi Yehoshua says this refers to Iyar." So you see that Cheshvan can be the second or eighth month, depending on your reference point.
Nissan is the first when counting the months (for kings or festivals) and Tishrei is the first when counting the years. To help you understand this, it is similar to the Western calendar today: January is the beginning of the calendar year while September is the beginning of the school year. So if you ask a child what number month October is he may say that it's the 10th month of the year or that it's the 2nd month of school. If you ask an accountant or businessman, he might give you a different answer based on when the fiscal year begins.
To turn to the Kabbalistic view of this matter for a moment: Nissan is when G-d created the world spiritually; Tishrei is when G-d created the world physically. However, this entails a much longer discussion.
I hope this was helpful to you.
*I.e. the year is reckoned to commence at different dates for different purposes, as the Mishnah goes on to specify.