Let's dive into this subtraction. We'll start with 587981 and subtract 6630 from it.

Step 1: We'll start by subtracting the digit 0 and the borrow 0 from 1 in column 1 and get 1.
1 is the first digit of our result.

Step 2: We'll start by subtracting the digit 3 and the borrow 0 from 8 in column 2 and get 5.
5 is the next digit of our result.

Step 3: We'll start by subtracting the digit 6 and the borrow 0 from 9 in column 3 and get 3.
3 is the next digit of our result.

Step 4: We'll start by subtracting the digit 6 and the borrow 0 from 7 in column 4 and get 1.
1 is the next digit of our result.

Step 5: We'll start by subtracting the digit 0 and the borrow 0 from 8 in column 5 and get 8.
8 is the next digit of our result.

Step 6: We'll start by subtracting the digit 0 and the borrow 0 from 5 in column 6 and get 5.
5 is the next digit of our result.

So, 587981 - 6630 = 581351.