Alright, let's solve this problem step by step. We have 588599 and 63077, 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 9 in column 1 and get 2.
2 is the first digit of our result.

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

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

Step 4: We'll start by subtracting the digit 3 and the borrow 0 from 8 in column 4 and get 5.
5 is the next digit of our result.

Step 5: We'll start by subtracting the digit 6 and the borrow 0 from 8 in column 5 and get 2.
2 is the next digit of our result.

Step 6: We'll start by subtracting the digit 0 and the borrow 0 from 5 in column 6 and get 5.
5 is the next digit of our result.

So, 588599 - 63077 = 525522.