Double-ikat weaving, known for its intricate geometric designs, is the hallmark of:

Patola
Khadi
Ajrakh
Zari

The correct answer is Patola.

Patola is a double ikat textile, which means that the warp and weft threads are tie-dyed before weaving. This results in a fabric with intricate geometric designs that are repeated on both sides. Patola is traditionally made in Gujarat, India, and is considered to be one of the most luxurious textiles in the world.

Khadi is a hand-spun and hand-woven cotton fabric that is traditionally made in India. It is a symbol of Indian independence and is often associated with Mahatma Gandhi. Khadi is a relatively simple fabric with a plain weave.

Ajrakh is a resist-dyed textile that is traditionally made in Gujarat, India. It is known for its intricate geometric designs that are created by using a resist paste to block out areas of the fabric before it is dyed. Ajrakh is often used to make clothing, home furnishings, and other decorative items.

Zari is a gold or silver thread that is used to embellish textiles. It is often used in Indian and Pakistani clothing, as well as in other decorative items. Zari is a very delicate thread and must be handled with care.

In conclusion, Patola is a double ikat textile that is known for its intricate geometric designs. It is traditionally made in Gujarat, India, and is considered to be one of the most luxurious textiles in the world.