Assume that by “four-digit positive integers” you mean 1000-9999.

The number of integers 1-9999 divisible by 3 is floor(9999/3)=3333.

The number of integers 1-999 divisible by 3 is floor(999/3)=333.

Therefore, the number of integers 1000-9999 divisible by 3 is 3333-333=3000.

The number of integers 1-9999 divisible by 7 is floor(9999/7)=1428.

The number of integers 1-999 divisible by 7 is floor(999/7)=142.

Therefore, the number of integers 1000-9999 divisible by 7 is 1286.

The number of integers 1000-9999 divisible by 21 is 429.

The number of integers 1000-9999 divisible by 3 or 7 is 3000+1286-429=3857.