Correct Answer: Demolish : Build

Solution : Given:
Heat : Cold→Heat is the feeling of something hot whereas cold means having a low temperature, not hot or warm. Thus, Heat and Cold are opposite of each other; the pair of words are antonyms.

First option: Encourage : Motivate; Encourage means to give hope, support or confidence to somebody whereas Motivate means to make somebody want to do something, especially something that involves hard work and effort. Thus, Encourage and Motivate are not antonyms.
Second option: Compete : Success; Compete means to try to win or achieve something whereas Success means the fact that you have achieved what you want. Thus, Compete and Success are not antonyms.
Third option: Sustain : Persist; Sustain means to keep somebody alive or healthy whereas Persist means to continue to exist. Thus, Sustain and Persist are not antonyms.
Fourth option: Demolish : Build; Demolish means to destroy something whereas Build means to make something. Thus, Demolish and Build are antonyms.

So, only the fourth option follows the same pattern as followed by the given pair. Hence, the fourth option is correct.