The Chalukyan temple complex known for its ornate carvings:

Pattadakal
Aihole
Halebidu
Belur

The correct answer is: A) Pattadakal

Pattadakal is a UNESCO World Heritage Site in Karnataka, India. It is a group of Hindu temples built by the Chalukya dynasty in the 7th and 8th centuries. The temples are known for their ornate carvings, which depict scenes from Hindu mythology.

Aihole is a village in Karnataka, India. It is known for its early Chalukyan temples, which were built in the 6th and 7th centuries. The temples are simple in design, but they are notable for their intricate carvings.

Halebidu is a town in Karnataka, India. It is known for its Hoysala temples, which were built in the 12th and 13th centuries. The temples are ornately carved and decorated, and they are considered to be some of the finest examples of Hoysala architecture.

Belur is a town in Karnataka, India. It is known for its Hoysala temples, which were built in the 12th and 13th centuries. The temples are ornately carved and decorated, and they are considered to be some of the finest examples of Hoysala architecture.

In conclusion, the Chalukyan temple complex known for its ornate carvings is Pattadakal.