In case you still don't know where the information you are looking for is even with the picture....The first square has the skein with the 4 on it. It is the second square that has your information. The square within that square represents a 4X4 inch (In American terms), or 10X10 cm (In UK terms) swatch. In the middle you see what are supposed to be a couple of straight knitting needles crossed over each other in an X. Under the needles it says "US 8" that is the needle size in the American system. And above the needles it says, "5mm", that is the size in the metric system.
What Cam said is very important. A size 8 needle is what someone had to use to get the gauge of 18 S (18 stitches) X 24 R (24 rows), it may not be what you would need to get the same gauge. And.... you can knit that same yarn to different gauges as well depending on the fabric you want or a designer used for a given pattern. So while the needle size given is helpful information, it may not be the needle you need for your project.
I think a lot of people buy the needle given and force themselves to get gauge with that needle. I don't think that is a good idea. It is better to develop a consistent feel for the way you knit and to get the gauge changes by changing either the needles or the yarn or both, depending on the situtation.
The needle size given on the label isn't really the `recommended' size, it's there to show what weight range the yarn falls in, or what part of the range for the weight which is what 2, 3, 4 or 5 is. Many patterns use a needle size either larger or smaller than that listed on the label, and a knitter should try to get the gauge listed on the pattern. This may also entail using a needle larger or smaller, whatever works for them.