Can I update my iPhone 4S on iOS 6 to iOS 8? I have new iPhone 4S with iOS 6.1.0. Can I upgrade my current iOS version to 8.0.2?

Whether there can be a problem that I skipped iOS 7 and jump straight from 6 to 8 version?
There won't be a problem.

I'm not 100% sure that upgrading to iOS 8 will be in your best interest, though, because I've seen lots of reports of people with 4Ss having performance problems on iOS 8.