trying to adjust the derailleur might help i had that problem with my 18 speed and i just adjusted the rear derailleur and it quit skipping
southern pride
When you shift to smaller rear cogs the derailleur has to pull the cable through the housing with spring tension in order to move. It does not take much to interfere with that movement. It is *not possible* for the lever to allow you to shift to 4th gear when in the 3rd gear position and also shift two gears, so *most likely* what is occurring is that you have moved the lever twice before the rear shifted, and there is excess cable friction that is delaying the shift. If you purchased the bike locally return it for a free adjustment. If not seek out a knowledgeable friend or a bike co-op for in-person assistance.
Not possible to see any problems as you are having from a pic. You did not mention before that the shift points ALL moved off one after you have the problem. That would indicate that your cable has "stretched," probably enough that it needs to be pulled through more. Just return it to the shop for correction and worry later about learning to make adjustments on your own. Also, return it again at the end of the 30-60 day free adjustment period, even if you are not aware of any problems.
your welcome i actually done what i said but hey different ways help alot better than anything
southern pride
You are unlikely to cause any damage till then. Just keep track of any other problems or concerns you have and convey them to the bike shop on Saturday.
Seems like basic derailleur tuning/tension. If that doesn't help, check the derailleur hanger for straightness. I did notice a scrape on that derailleur protector from the photo you posted. You can eye this but it will probably take a special hanger tool that screws on where the derailleur bolts on.
Best of Luck
GO RIDE...