In girl's clothing, a size 6x is a little bit longer and a bit larger in width than a size 6. It is comparable to a size 6 1/2, fitting somewhere between a size 6 and a size 7.
Seeing girl's clothing marked with a size 6x can be confusing, especially since other sizes like 4, 5, 7 and 8 are not found with the "x" designation. Age 6 is when many girls experience a growth spurt. This causes their height to increase rapidly and they often experience a change in weight as well. In order to bridge the gap between a size 6 and 7, girls' clothing manufacturers came up with the size of 6x. It is important to note that boy's clothing does not have a size 6x. This is because their growth patterns are not the same as those of girls the same age.
In addition to allowing the clothes to fit the girl better, implementation of a size 6x has an aesthetic reason as well. Most girl's clothing lines move from "little girl" styles into older styles at size 7. Therefore, if a 6-year-old girl needs clothing slightly larger than a regular size 6, a 6x will allow her to wear age-appropriate clothing.