Okay, let's tackle this math problem. We're starting with 688587 and subtracting 44125.

Step 1: We'll start by subtracting the digit 5 and the borrow 0 from 7 in column 1 and get 2.
2 is the first digit of our result.

Step 2: We'll start by subtracting the digit 2 and the borrow 0 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 1 and the borrow 0 from 5 in column 3 and get 4.
4 is the next digit of our result.

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

Step 5: We'll start by subtracting the digit 4 and the borrow 0 from 8 in column 5 and get 4.
4 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, 688587 - 44125 = 644462.