Mathcad Plus 6 is really a very old version!
But Mathcad 15 runs under Win10-64bit and should be able to open files created with your version.
Mathcad Prime (current version is 6) is PTCs infamous attempt to build Mathcad from anew on a newer code base (after all MC15 is more than 10 years old). Unfortunately PTC wasn't able to create a software which would be able to at least live up to old Mathcad, let alone surpass it. There a a few improvements in Prime but IMHO they don't by no means outweigh the disadvantages.
Prime is not able to read files created with real Mathcad, no matter which version. But you are given the ability to convert legacy sheets to the new Prime format. For the converter to work you need to have a full installation of a current version of Mathcad 15 installed in parallel to Prime. You can't buy Mathcad 15 but if you rent Prime you are also entitled to use Mathcad 15 using the very same license file. To give it a try you may download the trial version of MC15 - its the full version for 30 days and after that time it refuses to work. This in contrary to Prime which falls back to a still usable but limited "Express" version after the trial period.
So your options are:
1) Rent Prime and then just use Mathcad 15 which should be able to open and edit your files directly (give it a try with the evaluation version of Mathcad 15)
OR
2) Rent Prime, install Prime and MC15, convert all your worksheets to the new format and use Prime.
Some words of caution:
With option 1) you may find yourself in a dead end, as sooner or later PTC will drop maintenance and support for old Mathcad. As you cannot buy Mathcad/Prime but just rent it (typically for one year), chances are that future license files may not support real Mathcad anymore.
With option 2) you upgrade to a newer, more modern software, but in terms of functionality, ease of workflow, etc. its a downgrade in my opinion (maybe not, given that you start from a very old MC version). Furthermore you can't expect the converted worksheets to run without problems in Prime. You may have to manually post-process the converted files and maybe you'll find that some may not work in Prime at all. It depends on what features your sheets are using. You can testdrive the quality of the conversion using the evaluation versions of both Prime and Mathcad.
Good Luck!