Modern : antiquated : : weak : potent meager bond languid

In order to complete this analogy, first you have to understand the relationship between the first two words. Modern and antiquated are antonyms, which means they have opposite meanings. So in order to do this assignment, you need to provide an antonym of the word weak. In this case, the correct answer is potent, because potent means strong.
Meager means inadequate, bond is a noun and cannot be used here, and languid means sickly or weak, so that would be a synonym.