Macs format HDDs in a different filesystem, I think it is Ext2 or Ext3, something like that. Windows does not read this filesystem, it needs NTFS or FAT.
What to do? You can have your cousin partition the HDD on his machine, and put his mac files on a partition, also name that partition so it can be recognized later. Then he can format the other partition as NTFS (also rename it) and when you will plug that in a Windows PC it will see the NTFS partition and it will be able to access it. The other one will stay as it is, with his back-up files on it.