A number divisible by any number must be a multiple of the number itself. So we have to find the number of integers between 1-200 (as per definition set of positive integers excludes 0) which are multiple of 6 and 8.

Number of integers multiple of 6: N(multiples of 6)= 33

Number of integers multiple of 8:  N(multiples of 8)= 25

Probability of numbers divisible by 6: P(div by 6)=33/200

Probability of numbers divisible by 8: P(div by 8)=25/200

Thus P(divisible by 6 or 8)= P(div by 6)+P(div by 8) = 58/200

I hope my answer helps. All the very best for your future endeavors!