Generally speaking, the two eyes of each person cannot not move separately. However, in some cases, some people can move the two eyes seperately. Some people may train themselves to do this as a stunning skill just for fun. And some people maybe have got strabismus, so usually one of their eyes can stay fixed while the other one of their eyes look in a slant direction. If it is the latter condition, the person should go to the doctor's as soon as possible for an eye examination, maybe the doctor will treat it by a corrective apparatus. If the condition is serious, the person would have to take an eye surgery.
Well, generally speaking, if you have taken some practice, maybe you can achieve it. But on the other hand, in common, people cannot do it. Some research has shown that humans can indeed have some level of independent control of their eyes. And you should also need to know that many people have the ability to willfully "cross their eyes". In some cases, they can also move their eyes inward toward each other. But that can be rare, for our visual system is not suitable for binocular vision. Of course, you might be able to train yourself to move each eye independently. But it may just do no help to your eyes.