Which of the following sentences is hyphenated correctly?

A:The shelter gave him a two-year-old dog.

B:The day was terribly-cold.

C:You had an amazingly-good idea.

D:I only work part-time.

A:The shelter gave him a two-year-old dog.

Two-year-old is a hyphenated compound word. It is used as an adjective to describe how old the dog is.

Option B is wrong because we do not use hyphens between the adverb and the adjective it is describing.

Option C is also wrong for the same reason as option B.

Option D is incorrect as well. The reason is because the work is adjective phrase is after the noun it's describing rather than before.