You can't extend storage space on your iPad itself.
It's possible to upgrade iCloud storage. 5 GB are free, if you need more than that, you'll have to pay (50 GB, 200 GB, 1 TB, 2 TB are possible). Maybe your son was referring to this, when he told you about it. iCloud storage space is online, though, and doesn't help with your iPad's storage space.
6.5 GB is too much for system space. It shouldn't use more than 4 GB, afaik.
Did you try connecting your iPad to iTunes recently? If you haven't, do so and take a look at it's storage space using iTunes. You'll find something called "Other". If that's more than 2 or 3 GB, backup your iPad, and then restore it via iTunes. This should help getting rid of most of the Other storage.