Even-count tubular peyote stitch patterns can seem confusing at first glance. Not only are they flat representations of beadwork that is round, but they require that you "step up" to begin each new round — and that step-up shifts position in each round. However, once you understand exactly how these patterns work, you'll have them mastered in no time.
Start by examining the pattern above. You can tell that it's tubular (rather than flat) peyote stitch because it has a diagonal line of beads marked with X's. As a general rule, each of those beads represents the first bead in a round. With even-count peyote stitch, those X's also mark each bead that you pass through twice: once at the beginning of each round, and again at the end of each round. (This is the step-up.)
Note: Traditionally, the first low bead is considered to be the first bead in the first round, even though it is the second bead that you pick up. In some patterns, however, the first high bead is marked as the first bead. Either way, the marked beads in the pattern are the beads that you should step-up through at the end of each round.