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The external drive is formatted in NTFS. OS X can't write in NTFS disks.
You have different options, but the easiest is to install an application ilke Paragon NTFS. This app will allow you to copy your iTunes library to your external drive.
Another option is to format your external drive in a format that a PC and a Mac can write in. In this case, you can format it in exFAT or FAT32, and I suggest you FAT32 because I doubt you have files bigger than 4 GB in your iTunes library. If you have them, you will have to use exFAT, and you will have to format the external drive on a PC