How can we protect the woollen and silk clothes from the insects?

Is the above sentence correct?

Is he usage of "the insects" correct?

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It depends, Hanuman. As a first time question, meaning it comes out of the blue, ie. there's no previous context, then ENLs would not be likely to use either 'the'.

How can we protect woollen and silk clothes from insects?

This addresses the two things in a general sense; this is how they are viewed in these situations. For example;

1. Do you like the music I played for you yesterday?

2. Do you like music?

In 1. 'the music' has been introduced prior; both parties know which music is intended. It becomes immediately specific because the speaker adds information that clues the listener in.

In 2. we know that this is a first instance type question. Since there is no 'the', the listener is aware that the speaker is not talking about some prior shared info; it's new info. If there was a 'the' in 2, the listener would be perplexed because they would be wondering what "shared music" the speaker means.

Your sentence would fit in an extended conversation where both the insects and the types of clothes have been introduced already.