Okay, let's tackle this math problem. We're starting with 204259 and subtracting 98570.

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

Step 2: We'll start by subtracting the digit 7 and the borrow 0 from 5 in column 2 and get -2.
We add -2 to 10 and get 8 as the next digit of the result.

Step 3: We'll start by subtracting the digit 5 and the borrow 1 from 2 in column 3 and get -4.
We add -4 to 10 and get 6 as the next digit of the result.

Step 4: We'll start by subtracting the digit 8 and the borrow 1 from 4 in column 4 and get -5.
We add -5 to 10 and get 5 as the next digit of the result.

Step 5: We'll start by subtracting the digit 9 and the borrow 1 from 0 in column 5 and get -10.
We add -10 to 10 and get 0 as the next digit of the result.

Step 6: We'll start by subtracting the digit 0 and the borrow 1 from 2 in column 6 and get 1.
1 is the next digit of our result.

So, 204259 - 98570 = 105689.