Hi and Welcome. My Name is Ashik and I look forward to assisting you today with your question.
You can't delete the albums/photos which are synced from iTunes on the computer, from the iPhone itself. You have to delete the photos from the PC and then sync your iPhone then only it will be deleted from your iPhone.
FYI You can delete the albums that you created from the Camera Roll, from your iPhone itself.
On your PC, create a folder and name it anything (like My Albums). Then put all your albums (folders which contains the photos) in to that main My Albums folder. Now open iTunes and select your iPhone in iTunes (on top right or left under Devices). Click on Photos tab. Make sure "Sync Photos" is checked there. Select the My Albums folder that you've earlier created, in there. Select "Selected Folders" and then select the folders you want to sync.
If you delete any photos on your PC, it will be deleted from your iPhone also. If you put any new photos to My Albums folder, then it will be added to your iPhone as well.
Please let me know if that didn't work, so we can continue troubleshooting.