Empty and vacant denote absence of content or contents. Empty means without the appropriate or usual contents: an empty refrigerator; empty bottles. An empty room could be a bare room or one without people in it (the theater was almost empty). Vacant is usually applied to that which is temporarily unoccupied: a vacant position; three vacant apartments. A vacant lot is a piece of property which has no buildings on it and lies unused.
Combine and synthesize refer to mixing or joining together two or more things into one. Combine has the broader range of usage, and is looser with respect to how closely associated the joined elements become. Recipes instruct us to combine the diced onions, peppers, and spices in a bowl. Combine also applies to more abstract things: a major that allows her to combine her love of history with biology. Synthesize implies a transformative joining together. In science, it refers to the manufacture of a new substance by means of a chemical reaction between different elements (cells synthesize and secrete insulin). Outside of science, synthesize is mostly used for the mental work of bringing together a number of ideas, information, evidence, or data, in order to make sense of them as a whole (a paper synthesizing existing research). Similarly, a musician might synthesize styles from various musical traditions to create a new work.
Prudent and sensible both describe decisions and actions that show good judgment and practical wisdom. Sensible suggests the use of common sense, logic and reason, and practicality–a sensible policy, a sensible approach, sensible shoes. It’s a valuable attribute, although perhaps underappreciated, given that it can imply dull and boring, or practical at the expense of imagination, brilliance, desire, and fun. Prudent emphasizes carefulness, caution, and circumspection. A prudent course of action avoids risk, is mindful of the future, and doesn’t rush into anything. Prudent is frequently associated with wisdom in financial affairs (fiscally prudent, a prudent investment, prudent reserves).