No problem, let's work through this together. We're starting with 771978 and are subtracting 88003 from it.

Step 1: We'll start by subtracting the digit 3 and the borrow 0 from 8 in column 1 and get 5.
5 is the first digit of our result.

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

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

Step 4: We'll start by subtracting the digit 8 and the borrow 0 from 1 in column 4 and get -7.
We add -7 to 10 and get 3 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, 771978 - 88003 = 683975.