How many numbers from 1 to 600 are divisible by 4 or by 6 but NOT by 9?

Divisible by 4 or 6: 150 + 100 − 50 (by 12) = 200. Of these, the ones also divisible by 9 are multiples of LCM(4, 9) = 36 or LCM(6, 9) = 18; multiples of 36 are already multiples of 18, so just 600 ÷ 18 = 33. Answer 200 − 33 = 167.