Alright, let's solve this problem step by step. We have 820828 and 68966, and we're subtracting the second number from the first.

Step 1: We'll start by subtracting the digit 6 and the borrow 0 from 8 in column 1 and get 2.
2 is the first digit of our result.

Step 2: We'll start by subtracting the digit 6 and the borrow 0 from 2 in column 2 and get -4.
We add -4 to 10 and get 6 as the next digit of the result.

Step 3: We'll start by subtracting the digit 9 and the borrow 1 from 8 in column 3 and get -2.
We add -2 to 10 and get 8 as the next digit of the result.

Step 4: We'll start by subtracting the digit 8 and the borrow 1 from 0 in column 4 and get -9.
We add -9 to 10 and get 1 as the next digit of the result.

Step 5: We'll start by subtracting the digit 6 and the borrow 1 from 2 in column 5 and get -5.
We add -5 to 10 and get 5 as the next digit of the result.

Step 6: We'll start by subtracting the digit 0 and the borrow 1 from 8 in column 6 and get 7.
7 is the next digit of our result.

So, 820828 - 68966 = 751862.