IPhone – How to delete photos from the iPhone and still retain them on the desktop

• Connect your device to iTunes, select it in the left navigation bar.
• In the main screen, select the Photos tab.
• Check "Sync Photos" and select only the albums you want to sync. It will remove any pics on your iPhone that are not in the folder(s) selected on your PC

I'm not a PC guy but usually your photos live in iTunes Media Library. Whatever method you can use to find it, you delete your photos from there. Usually just use your search function on your PC to find the iTunes folder, open it until you find the iTunes Media Folder and delete whatever files you don't need to have synced.

After you delete your photos (Or just move them to another location if you're afraid you may loose them), you must sync your phone to iTunes again and this will refresh your iPhone's list of songs and photos, revealing more space. After this is done, find the option on iTunes to not sync your iPhone when connected and either manage your files manually or resync when your storage problem is fixed (a new phone with larger storage, for example). Your original photos are still in your PC, unless you deleted the originals.