Alright, let's solve this problem step by step. We have 724689 and 58081, and we're subtracting the second number from the first.

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

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

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

Step 4: We'll start by subtracting the digit 8 and the borrow 0 from 4 in column 4 and get -4.
We add -4 to 10 and get 6 as the next digit of the result.

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

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

So, 724689 - 58081 = 666608.