Okay, let's tackle this math problem. We're starting with 771129 and subtracting 82967.

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 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 1 in column 3 and get -9.
We add -9 to 10 and get 1 as the next digit of the result.

Step 4: We'll start by subtracting the digit 2 and the borrow 1 from 1 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 7 in column 6 and get 6.
6 is the next digit of our result.

So, 771129 - 82967 = 688162.