Alright, ready to do some subtraction? We're taking 413978 and subtracting 17477 from it.

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

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

Step 3: We'll start by subtracting the digit 4 and the borrow 0 from 9 in column 3 and get 5.
5 is the next digit of our result.

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

Step 5: We'll start by subtracting the digit 1 and the borrow 1 from 1 in column 5 and get -1.
We add -1 to 10 and get 9 as the next digit of the result.

Step 6: We'll start by subtracting the digit 0 and the borrow 1 from 4 in column 6 and get 3.
3 is the next digit of our result.

So, 413978 - 17477 = 396501.