When I am to reflect a current chessboard around say the horizontal line Y=4, would that imply that I need to reflect the bottom part to the top part, and then the top part to the bottom part?
It’s done all at once: each square is interchanged with its mirror image. Thus, you should interchange the top and bottom rows, the second and seventh rows, and so on. The square originally in the upper left-hand corner changes places with the one in the lower left-hand corner, the squares immediately to their right change places similarly, and so on.
Here’s a question to be sure that you’ve got it: After you’ve done the reflection, what’s happened to the colors of the squares, if anything?