Okay, let's tackle this math problem. We're starting with 878633 and subtracting 41278.

Step 1: We'll start by subtracting the digit 8 and the borrow 0 from 3 in column 1 and get -5.
We add -5 to 10 and get 5 as the first digit of the result.

Step 2: We'll start by subtracting the digit 7 and the borrow 1 from 3 in column 2 and get -5.
We add -5 to 10 and get 5 as the next digit of the result.

Step 3: We'll start by subtracting the digit 2 and the borrow 1 from 6 in column 3 and get 3.
3 is the next digit of our result.

Step 4: We'll start by subtracting the digit 1 and the borrow 0 from 8 in column 4 and get 7.
7 is the next digit of our result.

Step 5: We'll start by subtracting the digit 4 and the borrow 0 from 7 in column 5 and get 3.
3 is the next digit of our result.

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

So, 878633 - 41278 = 837355.