Foreigners often make some strange mistakes in Chinese when they study the most difficult language--- ---Chinese. We try to analyze typical sentences to correct these errors.

          Tāmen hěn ɡāoɡāo xìnɡxìnɡ de zǒu le.
False:他们很高高兴兴地走了。
          Tāmen ɡāoɡāo xìnɡxìnɡ de zǒu le.
True: 他们高高兴兴地走了。

“高高兴兴”是“高兴”的重叠形式，用作状语，表示动作（“走”）的状态。重叠以后的形容词含有程度加深的意味，不能再接受程度副词“很”的修饰。应删去“很”。
高高兴兴 is the reduplicative form of 高兴 serving here as an adverbial adjunct to the state of the action（走）. Reduplicated adjectives express intensification, and can no longer bemodified by an adverb of degree like 很. Thus, 很 in the sentence should be deleted.