I am not sure how to find out if the number is an integer or not I don’t need you to answer all those number that are in the pic I want to understand how to figure that out on my own

An integer number is a number that can be written without using a rational component. In other words, if a number can be written without using a fraction, then that number is considered an integer.
For example, let's take the first number:
[tex]-\frac{64}{8}[/tex]This number is written as a fraction. But, this is also equivalent to:
[tex]-\frac{64}{8}=-8[/tex]Since it can also be written without making use of a fraction then this number is an integer.
Also, there are numbers that are written in decimal form. For example:
[tex]-8.92[/tex]These types of numbers are not integers.