Let's get this math done. We have 677907 and 89703, and we're going to subtract the second number from the first.

Step 1: We'll start by subtracting the digit 3 and the borrow 0 from 7 in column 1 and get 4.
4 is the first digit of our result.

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

Step 3: We'll start by subtracting the digit 7 and the borrow 0 from 9 in column 3 and get 2.
2 is the next digit of our result.

Step 4: We'll start by subtracting the digit 9 and the borrow 0 from 7 in column 4 and get -2.
We add -2 to 10 and get 8 as the next digit of the result.

Step 5: We'll start by subtracting the digit 8 and the borrow 1 from 7 in column 5 and get -2.
We add -2 to 10 and get 8 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, 677907 - 89703 = 588204.