Alright, let's solve this problem step by step. We have 681193 and 11109, and we're subtracting the second number from the first.

Step 1: We'll start by subtracting the digit 9 and the borrow 0 from 3 in column 1 and get -6.
We add -6 to 10 and get 4 as the first digit of the result.

Step 2: We'll start by subtracting the digit 0 and the borrow 1 from 9 in column 2 and get 8.
8 is the next digit of our result.

Step 3: We'll start by subtracting the digit 1 and the borrow 0 from 1 in column 3 and get 0.
0 is the next digit of our result.

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

Step 5: We'll start by subtracting the digit 1 and the borrow 0 from 8 in column 5 and get 7.
7 is the next digit of our result.

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

So, 681193 - 11109 = 670084.