Stocking stitch (stockinette) right side up:
Upside down:
However, you can't simply flip a stitch upside down. A stitch is not the same on the bottom as it is on the top. A fundamental thing to note about knitted stitches is they are made out of a continuous series of loops. Each loop starts from the bottom, up over the needle, and back down.
Here's a simplified diagram of a row of stitches:
Notice in this picture there are 10 stitches (i.e., 10 bumps across the top):
The bottom of the row looks (almost) like a mirror of the top of the row. But look closely, and you'll see it's a mirror of the top shifted over one half stitch. When you are grafting using Kitchener stitch, or picking up from a provisional cast on, you need to be aware of this stitch anatomy. This means, when picking up stitches to work in the opposite direction, you need to compensate for the 1 stitch shortage by picking up a stitch from the edge. You can see this in action in How to cast on: working from a provisional cast on.
