Depending on your phone or tablet, you may find that playing directly from the Play Six Online page works for you.
On some devices, the virtual keyboard function or overall presentation on this page may be less than ideal to work with (or impossible!) in which case you can try one of the following third-party applications:
In the App store, search for Frotz. This IF-playing app is free and without ads. Download it.
Open it up and choose the Browse IFDB link at the top-left corner.
In the webpage that appears, enter "six" in the "search for games..." field, then press the question mark symbol to launch the search.
Choose the game's title to open its IFDB entry.
Choose the third link that appears, "Story File". This will download the game's story file, six.gblorb, into Frotz. You'll be returned to Frotz's list of stories and can now launch Six by choosing it there.
Last thing: Sometimes the game will say PRESS SPACE TO CONTINUE. Pressing the virtual keyboard's space key may not actually continue. All you have to do is press RETURN after pressing SPACE to send the space keypress through.
Fabularium is an IF-playing app for Android devices. It hasn't been updated since 2018, but I hear it still runs Six just fine. I don't have an Android myself to be able to test this, but all you need to do to try it is:
Search for the Fabularium app on Google Play.
Download the file six.gblorb from my site, and/or otherwise direct the Fabularium app to open or use it.