How are you launching LR 6? Are you double-clicking on the LR 6 icon? (By the way, the LR 6 icon doesn't say it is LR 6, but the LR 5.7 icon says it is LR 5.7)
What happens when you try to launch? If there is an error message, please quote the complete unedited word-for-word verbatim error message.
What is your operating system?
My system is a MacBook Pro Retina running OS X Yosemite. I have several LR catalogs located on several external hard drives. My LR app is located on the mac's internal hard drive. With LR5 and previous LR versions I'd open the external drive and double click the LR catalog (*.lrcat) on the external drive. That always launched the LR app on the mac's internal drive. In fact LR 5 catalog sill launches the LR 5 app. But with LR 6 double clicking the catalog on the external drive does nothing. No messages. However, if LR 6 is already launched double clicking will terminate the program that's running and relaunch with the appropriate LR 6 catalog.
The problem, I believe, is that simply click the catalog on an external drive will not launch LR 6 on mac's internal drive.
This was not the case with previous versions of LR
The catalog files (.LRCAT) are associated with one program, and that must be Lightroom 5. It has nothing to do with the drive that things are stored on.
Not being a Mac expert, I can't say for sure if there is another way to handle this ... but it seems to be that to open the LR 6 catalog, you must find the LR 6 application and launch that and then use File->Open Catalog and point to the LR 6 catalog of interest.
You might consider upgrading all the catalog to LR 6, which would mean you could uninstall LR 5 and eliminate this problem forever. If you need to have the catalog as LR 5 for some reason, then this isn't possible. To make your life even easier, you could merge all catalogs into a single catalog.
I have converted all of my LR 5 catalogs to LR 6. None will launch LR 6 from an external drive if LR 6 is not running. However, all will relaunch to the appropriate catalog if LR 6 is running. Even more important, I just discovered that double clicking the LR 6 catalog located on the mac's internal drive also fails to launch the app.
Give a try on your system. Double click the catalog without LR running and see what happens.
Have you uninstalled LR 5?
Have you tried to associate LR 6 with the file extension .LRCAT?
I have not uninstalled LR 5.
I'm not certain how to associated LR 6 with the file extension. Can you further explain?
Since I do not own a Mac, I cannot explain further. I'm sure that there are others in this forum who will drop in and explain. Or you could try your favorite search engine.
Thanks again. I found out how to associate .lrcat with LR 6 and that fixed the problem.