How do I adjust the rear gears of a bike that will not change to higher gears? It is stuck in lower two or three gears.
By higher gears I assume you mean smaller cogs on the back, which are higher ratio gears. Usually your derailleur won't go there it's because of cable friction, although you could have a bent derailleur or derailleur tab.
If you remove the cable from the derailleur it should drop down into these gears. If not it's probably due to a bent hanger or derailleur. If you can physically shift the derailleur to all the cogs with your hand on the derailleur then you should change the cable. I'm assuming that your gears used to all work and that you haven't messed with the limit screws.
A good way to check your limit screws is with the cable detached from the derailleur and then push the derailleur with your hand as far inside as it can and let it drop as far as it will. This completely eliminates cable friction.
With the cable attached to the rear derailleur I like to shift the derailleur into the smallest gear in the back and then grab the cable that goes to it as it runs down the downtube and pull it until the derailleur shifts to the biggest rear gear, this is the best way test for the L limit screw and it prestretches the cable, so won't have to adjust it as soon. I learned this from a Mavic neutral support mechanic.