When you knit in the round, you do read the chart from right to left for every row.
The red box on the chart is usually the pattern repeat--the stitches in it are the same as the stitches outside of it. It just contains the number of stitches in the "pattern" part of the stitching.
So you would knit your stitches up to the red box, knit the stitches within the red box as many times as will fit around the sock, and then knit the stitches after the red box for the last stitches on your row. Does that make sense?
So my X's are the stitches you start with, you'd knit the xoxoxox as many times as you can and when you're done with the last complete repeat, you'd have 4 XXXX left to work if my diagram was a real pattern.
I hope this is clear.