Lightroom 6. Access

You want a supported Adobe product that will be supported in the future: you subscribe. Simple.

Adobe have decided aribrarily to stop supporting Lightroom 6.

It wasn't arbitrary, Adobe stops supporting all old software at some point, this is a common practice for Adobe and many other software companies. This fact that Lightroom 6 is unsupported is not new, this was announced in the last month or two of 2017. And just because it isn't supported, Lightroom 6 still runs on most operating systems.

Is there and alternative proposed by Adobe or is the only option is to purchase another subscription?

You can keep using unsupported software. You can upgrade (subscription). You can use software from other manufacturers. You have lots of choices.

I've moved this from the Using the Community forum (which is the forum for issues using the forums) to the Lightroom Classic forum so that proper help can be offered.