Step 1: Reading the question. We need the term for seeds that start to grow while still hanging on the parent plant.
Step 2: The meaning. Sometimes a seed does not wait to fall off. It germinates and forms a young seedling while still attached to the mother plant.
Step 3: The correct word. This special habit is called vivipary. It is commonly seen in mangrove plants that live in salty, muddy soil.
Step 4: Why the others do not fit. Embryogenesis is just the growth of the embryo. Syngamy means the fusion of male and female gametes. Parthenogenesis means an embryo forms without fertilization. None of these mean germination on the parent.
Step 5: Final reasoning. Only vivipary matches the description given.
Step 6: Conclusion. Therefore the correct answer is "Vivipary". \[ \\boxed{\\text{Vivipary}} \]