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The word "熬出头" is formed by combining the character 熬, meaning to endure or suffer through, with 出, indicating emergence or exit, and 头, which here denotes an endpoint or conclusion; this structure creates a verbal phrase that literally translates as "endure until coming out to the end", conveying the figurative meaning of finally overcoming a long period of difficulty.

Word Definition - 熬出头

áo chū tóu to break clear of all the troubles and hardships; to achieve success; to make it