For this problem, make use of the fact that for sets A and B, |A U B| = |A| + |B| - |A ∩ B|.
For integers between 1 and 1000, how many of them are divisible by 3 or 8? How many of them are divisible by 4 or 6?
For integers between 0 and 999, how many of them has 3 or 8 as one of its digits?
(For example, 90 does not have 3 or 8 as one of its digits but 830 contains both 3 and 8.)