To educe something means to draw it out — you can also say “elicit,” or depending on the situation, more nuanced synonyms might be “evolve” or “evoke.” “Educe” comes from the Latin “ducere,” meaning “to lead,” and the “e-” prefix in this and all of the related options is used to form verbs expressing the inducement of a state. The verb “educe” has an interesting connection to the verb “tow,” which is a more physical representation of the drawing out concept, meaning “to drag or pull along.” The Greek “daidussesthai,” meaning “to drag” turned into the Latin “ducere” (“to lead, draw”), which became the Gothic “tiuhan” (“to draw, pull”). That turned into the Old English “tēon” (“to draw, pull”), which eventually evolved into “tow.”