When selling used goods, people sometimes use phrase 'used twice' or 'never used' to answer questions like 'How many times have you used it'.
Is there any formal phrase for this case if 'number of use' is not correct one to describe it?
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It is unclear to me why you would have to use such a construction at all, but "extent of wear" might be an equivalent. You need to specify in what kind of a sentence you want to use this.
"Number of use" is incorrect because "use" is not a countable noun. E. g., "the reason behind her constant use of the phone was sitting beside her" [source]
"Number of uses" would be correct, because now we are using a different sense of the word "use", one in which it is countable.
However, when I'm buying something used, I rarely expect the person selling it to remember exactly how many times s/he used it. I would ask this person,
Has this item been used a lot?
If you are selling something, you would say "only slightly used."