Hey there!
Answer:
I think that what the given sentence is missing is a comma and a word correction.
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"Mitch was worried that his car might break down after he noticed a quite clucking sound."
First of all, "quite clucking sound." makes no sense, however "quiet, clucking sound." does. Hence, the given sentence just needs a comma and the word "quite" to be changed to "quiet".
Hope this helps!