I have iPhone 4 and won't let me update my software?

5.5 GB used 882 MB Available update requires at least 2.5 GB of available storage I don't I have room to update my iPhone? I forgot to said I deleted all my pictures and most of my music off my iPhone still won't let me update iOS 6 If anyone can help me with this my e-mail address is jocelinelheureux@hotmail.com thanks.

Not much you can do but to make room. The iOS firmware is flashed to the device, and all of the work is done on the device, then the IPSW is removed after everything is completed. If you don't have enough space for the IPSW you can't upgrade. Simple as that.

Just take backup of your Data into iTunes. Or using iTools…
Then Update it.