(A) is a technique of vegetative propagation in which a part of the stem or a young branch of a plant is pulled and buried in moist soil, such that the branch is still attached to the Parent Plant. After some time, roots develop in the buried part and it grows into a new plant. (B) is an example of plant usually grown through this technique. (A) and (B) respectively are :

The correct answer is Layering, Jasmine.

Step 1: Understanding Statement (A)
The process described in statement (A) involves pulling down a part of a stem or a young branch of a plant and burying it in moist soil while keeping it attached to the parent plant. Over time, adventitious roots develop from the buried segment, allowing it to be separated and grow into an independent plant. This specific artificial vegetative propagation method is known as Layering.

Step 2: Identifying Example (B)
Plants with flexible and low-hanging stems are commonly propagated using layering. A classic example of a plant propagated by layering is Jasmine (as well as plants like strawberry and raspberry).

Step 3: Evaluating the Options
- Layering, Jasmine: Correctly identifies the technique (A) and the example plant (B).
- Cutting, Potato: Cutting involves completely detaching a stem or leaf section first, not leaving it attached to the parent plant.
- Grafting, Rose: Grafting involves joining the stem (scion) of one plant onto the rooted stock of another plant.
- Budding, Hydra: Budding in Hydra is an animal reproductive process, not a plant vegetative propagation technique in soil.

Therefore, (A) and (B) respectively are Layering, Jasmine.