Why won’t my iphone update

Use (the current version of) iTunes.

Update your iPhone, iPad, or iPod touch - Apple Support

If that doesn't solve it, tell us exactly what you tried, what symptoms of failure you have seen, what steps have succeeded, and version numbers of iOS, iTunes, and your computer's operating system name and version number.

Difficult to say why, since you do not provide any information about what it does when you try. Either way, see this for instructions on updating, and there is also a link at the bottom for troubleshooting over the air updates. Update your iPhone, iPad, or iPod touch - Apple Support

If you are still unable to update, try this one, If you can't update or restore your iPhone, iPad, or iPod touch - Apple Support. And if necessary, you can come back with additional information for help.

Buying more space from Apple is iCloud storage, which has nothing to do with the storage space on your device. The first document contained a link for dealing with issues with space and over the air updates. However, at this point, your best bet is to update the device with the computer and iTunes, as is also provided in the document provided. You need twice as much space to update the device over the air since it has to unpack on the iPhone, which takes up space. Doing it on the computer allows it to unpack on the computer, thus not taking the larger amount of space. Use the computer and iTunes, following the instructions in the support document I provided.

Glad it’s working for you now. Always keep your iPhone storage with at least 10% of its total storage free. (Settings > General > iPhone Storage).

Enjoy your Apple gear.

To add to ChrisJ4203’s excellent remarks, not only have you not told us whether you have already tried to use iTunes to perform the update, but you have also not told us your iTunes version number in case you have tried. You need a current version of iTunes which requires a reasonably current operating system version to communicate to iOS 12 devices.

You're welcome.