What do I do to resolve "Partition failed...error: Couldn’t modify partition map because file system verification failed"?

My computer is a late 2009 MacBook Pro, 500GB hard drive divided across 2 partitions 1st/top partition is 400GB with Mavericks installed, and 2nd partition is 100GB with Snow Leopard installed (a 'backup' snow leopard bootable partition, with only 34GB used and 68GB available, which I generally don't use and don't need).

My backup hard drive - 500 GB Lacie had two partitions. The first/top partition - MB Pro - was approx. 460GB and contains my Time Machine (TM) backups of my late 2009 MacBook Pro hard drive (2 partitions) (see screen shot of backup folder). There was a second partition called MB Pro 2, none of which was being used - the partition was completely blank.

I decided to delete that 2nd partition on the Lacie external HD to gain space for my TM backups on the "MB Pro" #1 partition. I thus deleted the 2nd partition on the Lacie. Then I dragged the slider down to increase partition #1 to take up the now unused space on the backup hard drive.

After 15-20 minutes, Disk Utility gave the following message:

"Partition failed with the error:

Couldn’t modify partition map because file system verification failed."

What has happened?

How can I get those 40GBs back? MB Pro, partition #1 reads 460GBs. But the Lacie is a 500GB hard drive.

Please advise and thanks!