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  • I think it depends on the context to decide which question to use. We use the question without the article "the" when we want to brainstorm different ways of implementing an activity; but when the methods to carry out the activity are known to both questioner and answerer(s) and what they need to do is to pick out the good ones, then the question with "the" should be used.

  • What are good ways of doting this?

    This correct, here are "good ways" mean the good ways in general.

    but when it is said with 'the' whcih is also correct, but this
    time there is some 'particularity' about the 'good ways'.

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