We need to find How many integers between 10 and 20, inclusive, have a remainder of 1 or 2 when divided by 3

Now, any number when divided by 3 will give us 0, 1 or 2 remainder
Only those numbers which are multiples of 3 will give us 0 remainder, others will give us 1 or 2 remainder

=> Between 10 and 20 we can exclude all the multiples of 3 to get the answer

=> Exclude 12, 15, 18 => 3 numbers

=> Numbers which will give a remainder of 1 or 2 when divided by 3 = (20 - 10 + 1) - 3 = 8

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Remainders