If you want to transfer files from a Mac to Windows PC and vice versa using an external portable hard drive then you have to have the external drive formatted in a file system both OS's can read and write too. Your choice is ms-dos (aka fat32) or exfat and I go over the difference in the video.
Note: most external drives you buy will automatically be formatted in NTFS which is a Windows file system. Macs can only read but not write to a ntfs file system. So if you want your external hard drive to be backward compatible with both OS's then you need to reformat it with fat32 or exfat.