The number of positive integers less than 2018 that are divisible by 6 but are not divisible by at least one of the numbers 4 or 9 is

There are $$\left\lfloor\frac{2017}{6}\right\rfloor=336$$ positive integers less than $$2018$$ divisible by $$6$$. A number divisible by both $$6$$ and either relevant divisibility condition contributes through multiples of $$36$$, of which there are $$\left\lfloor\frac{2017}{36}\right\rfloor=56$$. Thus the required count is $$336-56=280$$.