How to delete photos on iOS 6

To delete photos and videos from your device

To delete synced photos and videos

1. In iTunes, select the device icon in the Devices list on the left. Click the Photos tab in the resulting window.
2. Choose "Sync photos from."
   • On a Mac, choose iPhoto or Aperture from the pop-up menu.
   • On a Windows PC, choose Photoshop Album or Photoshop Elements from the pop-up menu.
3. Choose "Selected albums" and deselect the albums or collections you want to delete.
4. Click Apply.

To delete Camera Roll photos and videos

There are two methods to delete items from the Camera Roll:

Import the Camera Roll to your computer, choosing to delete items after import.

or

Delete photos and videos from your device manually. Open the Photos application, open the Camera Roll, tap the Action button, tap each photo to select it, and tap the Delete button.
Note: For photos and videos you want to save for later, import them to your computer before deleting them from the Camera Roll.

http://support.apple.com/kb/HT4236

photos synced to the iPod are not included in the backup that iTunes or iCloud makes.