How do I back up all my photo library on to 2 x Toshiba hard drives from Mac book pro?
All I get when trying to move, even a few photos at a time is a no entry sign! Very frustrating
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Mac includes a very capable backup system called Time machine.
Time machine works quietly and automatically in the background, without interrupting your regular work, and only saves the incremental changes (after the first full backup). Time machine backs up every connected drive that is in a Mac compatible format. It can not back up Windows format drives.
Time Machine's "claim to fame" is that it is the backup that gets done, because it does not ruin performance of the rest of the computer while doing its backup operations. You do not have to set aside a "Special Time" when you only do backups. When you need it, your Time machine Backup is much more likely to be there.
Back up your Mac with Time Machine - Apple Support
If you choose to connect a second drive, Time machine will create a second, independent backup set on the other drive, and alternate: every-other backup goes to every-other drive.