If there were no more photosynthetic organisms, there would be no more food for the animals that eat them. These animals would then starve to death. The animals that eat those animals would also starve to death, and so on. Eventually, all animals would die.
In addition to providing food, photosynthetic organisms also produce oxygen. Oxygen is essential for respiration, the process by which animals convert food into energy. Without oxygen, animals would not be able to breathe and would quickly die.
Therefore, if there were no more photosynthetic organisms on Earth, all animals would eventually die.