【Favor】 , 【countenance】 , 【encourage】 are comparable when they mean to give the support of one′s approval to.
【Favor】 may be used in reference to a well-disposed inclination, an expressed preference, or active support or sometimes to a circumstance or agency conducive to a result.
【Countenance】 may indicate mere toleration; more often it implies a positive favoring.
【Encourage】 carries the notion of heartening stimulation, inciting or inducing especially by expressions of approval, confidence, liking, or comfort.