I wanted to know what kind of stitch is shown in this picture. Can I make it with a brother sewing machine cs6000i?
The overlock stitch is a combination of a straight stitch and a zigzag. It sews backwards and forwards in a straight line, but between every set of straight stitches, it sews a zigzag. If done correctly, this resembles serging, which is how most store-bought clothes are sewn. (Yesterday's Thimble)
And it looks like there are a few different overlock stitches on the Brother CS6000i! To get that very compressed look as in your example picture, you would want the stitch length to be pretty short in comparison to the width. As always, experiment with a few sample pieces of fabric before you put your final piece through!
I personally think this is an overlock stitch, however, I may be wrong!
The latter of this question I can answer though... Yes, the Brother CS6000i does allow an overlock stitch. I own a Brother CS6000i myself and can confirm this.
If you already know about the Brother CS6000i then you can ignore this part, but there is a review of it here (unfortunately it does not seem to mention the different types of stitches) but it gives a decent insight into the Brother CS6000i. Anyway I hope I helped in some form or another, I am not an expert in sewing (Still learning :P)