Alright, let's solve this problem step by step. We have 684880 and 25507, and we're subtracting the second number from the first.

Step 1: We'll start by subtracting the digit 7 and the borrow 0 from 0 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 0 and the borrow 1 from 8 in column 2 and get 7.
7 is the next digit of our result.

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

Step 4: We'll start by subtracting the digit 5 and the borrow 0 from 4 in column 4 and get -1.
We add -1 to 10 and get 9 as the next digit of the result.

Step 5: We'll start by subtracting the digit 2 and the borrow 1 from 8 in column 5 and get 5.
5 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, 684880 - 25507 = 659373.