How many of the first 200 positive integers are multiples of neither 6 nor 15

There are

... floor (200/6) = 33 multiples of 6

in the range 1 ... 200.

There are

... floor (200/15) = 13 multiples of 15

in the range 1 ... 200, half of which are also multiples of 6.

So, there are 33 + 13 - 6 = 40 numbers in the range 1 ... 200 that are multiples of either 6 or 15 or both.

The remaining 200 - 40 = 160 numbers are not multiples of either.