Introduction:
In this analogy, we are given the word "venerate" and its relationship with the word "worship." We are then asked to identify the word that has a similar relationship with "extol."

Understanding the analogy:
To solve this analogy, we need to understand the relationship between the words in the given pair. "Venerate" means to regard with deep respect or reverence, while "worship" means to show reverence and adoration to a deity or religious figure. Thus, "venerate" is a type of reverence or respect, and "worship" is a specific form of reverence.

Identifying the relationship:
To find the word that has a similar relationship with "extol," we need to identify a word that is a type of praise or admiration, just as "extol" is a specific form of praise.

Options analysis:
Let's analyze the given options:

a) Homage: Homage means showing respect or honor towards someone or something. While it is related to reverence, it does not specifically mean praise or admiration. Therefore, option A is not the correct answer.

b) Glorify: Glorify means to praise or honor something or someone. This word is a direct synonym of "extol" and represents a similar relationship as "worship" does with "venerate." Thus, option B is the correct answer.

c) Recommend: Recommend means to suggest or endorse something or someone. This word does not represent the same relationship as "worship" does with "venerate." Therefore, option C is not the correct answer.

d) Complement: Complement means to complete or enhance something. While it can be related to praise or admiration in certain contexts, it does not represent the same relationship as "worship" does with "venerate." Therefore, option D is not the correct answer.

Conclusion:
Based on the analysis, we can conclude that the correct answer is option B, "glorify." This word shares a similar relationship with "extol" as "worship" does with "venerate," representing a specific form of praise or admiration.