Your license allows you two installations of the program on your computers. You will, of course, have to download the PC version for your Windows computer and the Mac version for your OSX -- but you will use the same serial number for both.
You might want to consider purchasing Premiere Elements 14 from an authorized reseller in the box packaging. In that case, you get an installation disc for Windows and an installation disc for Mac at a lower price than if you purchased individually, Premiere Elements 14 Windows download and Premiere Elements 14 Mac download. In that case of the box packaging purchase, I believe that is the scenario where you use the same serial number for each Windows and Mac install.
Adobe direct sells only the download which is specific to the computer to which it is downloaded.
I believe that the Adobe License reads that you are allowed to have the same purchased activated serial number on no more than 2 of your computers. And, then you are supposed to run one at a time. Depending on your video work plans, two different serial numbers might be more expensive but would have its perks in this regard.
Please consider and compare.