What if you recive an embarrasing request?

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It is inevitable that someone ask for help from you. However, occasionally, it's not convinient for you or you just don't want to give a hand, but it is not easy to say no to them becasue they maybe your friend or even your boss. For me, I will have to find an excuse and refuse them in polite words. Anyway, what may occur is that you are really in urgence and have to say no. So how do you handle such embarrasing request?