Iphone 4 rear camera doesn`t work

First make sure you make a backup of your phone in itunes (use ht1766 from Apple support site) then transfer your purchases from the phone to itunes(click on file then transfer purchases) then try to restore the phone software to make sure it is not just a software issue. Then test the phone after you have restored it. If still having the same issue then it is a hardware issue, and it will need to be serviced. If you still have warranty coverage it will be free, if not it will be a $199 Out of Warranty fee to have the phone serviced.

First try restart, then reset.

If those fail, then try restore as described above.

First try one of these methodes:

Try to restart your iPhone
Hold the power button and slide to turn off, then turn it on

if you still have the same problem then try the second methode:

Reset Settings of your device:
Settings>> General>> Reset >> Reset All Settings
Make sure you reset only your settings and NOT any other Contents

if you still have the same problem, so it seems to be a hardware issue, take it to the nearest Apple Store.

Kind regards