The homework question is to name all the sets of numbers to which each number belongs and we are suppose to name as many as possible. THe first number is negative square root of 64.
If you simplify the square root of 64, you get 8. So you are really looking at negative 8. This is an integer, rational number, and real number. All integers are rational numbers and all rational numbers are real numbers.
Rational numbers are numbers that can be written as fractions, like 1/3 or 4/5. This includes negative 8, because we can write it as -8/1.