If an intangible asset has a legal life of eight years but contractually the usefulness is limited to six years, a company will amortize the cost over:

The company should amortize the cost over Intangible Asset's useful life (being shorter than it's legal life) i. e six years

Explanation:

Intangible assets have a useful life which is either identifiable or indefinite. Intangible assets with identifiable useful lives are amortized on a straight line basis over their economic or legal life, whichever is shorter.

Under cost basis, Intangible assets are amortized over a specific number of years regardless of the actual useful life of the asset.

As per the information provided in the given case, legal life of the intangible asset is eight years but contractually it's usefulness is limited to six years.

Therefore the company shall amortize the cost over the shorter of the intangible's useful life and it's legal life i. e six years.