Okay, let's tackle this math problem. We're starting with 976513 and subtracting 20777.

Step 1: We'll start by subtracting the digit 7 and the borrow 0 from 3 in column 1 and get -4.
We add -4 to 10 and get 6 as the first digit of the result.

Step 2: We'll start by subtracting the digit 7 and the borrow 1 from 1 in column 2 and get -7.
We add -7 to 10 and get 3 as the next digit of the result.

Step 3: We'll start by subtracting the digit 7 and the borrow 1 from 5 in column 3 and get -3.
We add -3 to 10 and get 7 as the next digit of the result.

Step 4: We'll start by subtracting the digit 0 and the borrow 1 from 6 in column 4 and get 5.
5 is the next digit of our result.

Step 5: We'll start by subtracting the digit 2 and the borrow 0 from 7 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 9 in column 6 and get 9.
9 is the next digit of our result.

So, 976513 - 20777 = 955736.