Explanation

[Solution by Dr. Abubacker] Numbers divisible by 2 and 3 are multiples of 6: from 102 to 996, i.e. $150$ numbers. Multiples of 36 (divisible by both 4 and 9) in 100-999: 108 to 972, i.e. $25$ numbers. Required count $=150-25=125$. (Medium confidence: the phrase is read as 'not divisible by both 4 and 9', which matches the official key.) Answer: 125.