I brought a seagate backup +slim hard drive today. I want to make partition in this but overtime I click on it the partition button( greys out)?

I would suggest that you need to start by using Disk Utility to erase and reformat the entire top-level drive:

This will erase the ~500Mb data on the existing partition, so if it's valuable content you'll need to back it up first.

From there you can partition the top-level drive.

That's both because the file system on the drive now is an NTFS partition and because you need to select the device to partition it.

If you select the "Seagate BUP" device you should be able to partition it, though you may need to delete the "akash seagate" NTFS partition first.

Click on the part I have highlighted, and you should be able to erase and repartition the drive