If you buy LR6 from a re-seller or on-line store the boxed version with disks can be installed on both Windows and Mac. You can still use the download links to install, and then use the serial number from the inside white cardboard box.
However, you should be aware that each major version of LR (1, 2, 3 etc) has its own variation of the catalog file, *.lrcat, and cannot directly support another version's catalog. So if you attempt to open an LR4 catalog in LR6, it will ask if you want it to make a copy of the catalog and then convert the copy to be LR6 compatible. I don't know what will happen if you do it the other way, feeding an LR6 catalog to LR4 - never had reason to try it - but at a minimum LR4 could not create the effects that are unique to 5 and 6. Since the license covers two installations, it would be best to have LR6 on both machines, provided the Windows system is not too old to support LR6.