Can't save jpeg files to seagate hd with previous files from pc

I am trying to save reworked raw and psd files as jpegs into a seagate hd and I'm getting an error message that reads

no permission or authnorization to save. The hd was used on my pc and i need to use it between my pc at work and my mac at home.

What can i do to use one hard drive with the two machines?