You should find somewhere in the Menu system that the inbuilt Styles have protection applied to them. Try turning off the protection, make the changes and then save.
If this is not possible then make the changes and save the Style to a User Bank (check the manual you may have to Copy and Paste the Style to a User Bank first).
Or
Use the Songbook feature by saving the customised Style there as a Song.
I am hoping this all works for you, I do not have a Yamaha SX but had a Korg Pa (vastly superior imho) and everything on that Arranger was quick and easy to do and to call up saved Registrations.
The SX tutorial videos may also help
Take your performance to a whole new dimension with the PSR-SX. Replacing the hugely successful PSR-S series, the PSR-SX900 is the new generation in Digital Workstation sound, design and user experience. These instruments will inspire and intensify your musical performance and enjoyment.
uk.yamaha.com
Korg UK do a live and interactive Webinar every month and about twenty are now available to view, maybe Yamaha do something similar.
PS
Do backup your operating system and user data before making any changes and then again after you have saved new data to User Banks.