Okay, let's tackle this math problem. We're starting with 409144 and subtracting 6886.

Step 1: We'll start by subtracting the digit 6 and the borrow 0 from 4 in column 1 and get -2.
We add -2 to 10 and get 8 as the first digit of the result.

Step 2: We'll start by subtracting the digit 8 and the borrow 1 from 4 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 8 and the borrow 1 from 1 in column 3 and get -8.
We add -8 to 10 and get 2 as the next digit of the result.

Step 4: We'll start by subtracting the digit 6 and the borrow 1 from 9 in column 4 and get 2.
2 is the next digit of our result.

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

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

So, 409144 - 6886 = 402258.