Possible answers could include:
1. The greatest achievement of the Incas was the construction of their vast and advanced network of roads and bridges. This enabled them to efficiently communicate, trade, and administer their empire over the rugged terrain of the Andes mountains. The engineering feats required to build these roads and bridges showcased the Incas' impressive organizational skills and technological capabilities.
2. Another significant achievement of the Incas was their agricultural practices, particularly their development of terraced farming. By constructing terraces on the steep mountainsides, the Incas were able to maximize arable land for cultivation. This innovation allowed them to support a large population and provided resilience against environmental challenges such as droughts or floods.
3. The Inca Empire's administrative and political system, known as the Tawantinsuyu, was also a remarkable achievement. It was a highly centralized and organized system that effectively governed a vast territory and diverse population. The Incas used a system of government officials, known as the mit'a, to oversee various aspects of society, including taxation, labor allocation, and infrastructure projects.
In conclusion, while it is subjective to determine the single greatest achievement of the Incas, their road systems, agricultural practices, and political organization all played crucial roles in their success and longevity as a powerful empire in the Andes region.