The stuff in the curly brackets or braces tells us how exactly to fill up the set A. In other words, it tells us how to list the elements.
We're told that x is an integer. So it's a whole number that is negative or positive or 0. We're also told that x is between -6 and 0; we include -6 and exclude 0. This is because of the "or equal to" that is associated with the inequality sign next to -6 but the 0 has no "or equal to" for its inequality sign.
Putting all the pieces together, we get this answer: {-6, -5, -4, -3, -2, -1}
Notice how -6 is in the list but 0 is not