Can iOS 13.0 or later be downloaded in an iPhone 6?

If there is an app that you want to use that requires a newer iOS version than what's compatible with your iPhone, then the only solution is to get a newer iPhone that can run the required iOS version..

or reach out to the developer of the app(s) and ask them to support older iOS versions (which isn't likely going to happen if they've dropped support)

no it cannot

If we can’t download iOS 13.0, what do you suggest for us to be able to download apps (i.e. Kroger app and etc)?

cherproffitt74 wrote:

If we can’t download iOS 13.0, what do you suggest for us to be able to download apps (i.e. Kroger app and etc)?

I suggest you go buy a new phone. Yours is obsolete.