Okay, let's tackle this math problem. We're starting with 618682 and subtracting 41619.

Step 1: We'll start by subtracting the digit 9 and the borrow 0 from 2 in column 1 and get -7.
We add -7 to 10 and get 3 as the first digit of the result.

Step 2: We'll start by subtracting the digit 1 and the borrow 1 from 8 in column 2 and get 6.
6 is the next digit of our result.

Step 3: We'll start by subtracting the digit 6 and the borrow 0 from 6 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 8 in column 4 and get 7.
7 is the next digit of our result.

Step 5: We'll start by subtracting the digit 4 and the borrow 0 from 1 in column 5 and get -3.
We add -3 to 10 and get 7 as the next digit of the result.

Step 6: We'll start by subtracting the digit 0 and the borrow 1 from 6 in column 6 and get 5.
5 is the next digit of our result.

So, 618682 - 41619 = 577063.