Q: Can't update iOS 6.1.3 to 9.2.1 and I have 8 g free

What kind of error message do you get?

And how are you trying to update?  Over the air or with iTunes?

Since you skipped tow major new releases it would be much safer to download the installer to a computer with iTunes and install the update using iTunes than doing it over the air.

See this discussion:  I am trying to upgrade my iphone 5 from iOS 6.14 to iOS 9.2.1 and I m getting the below error:unable to install update an error occurred installing ios 9.2.1, Please help!!