Okay, let's tackle this math problem. We're starting with 82426 and subtracting 39095.

Step 1: We'll start by subtracting the digit 5 and the borrow 0 from 6 in column 1 and get 1.
1 is the first digit of our result.

Step 2: We'll start by subtracting the digit 9 and the borrow 0 from 2 in column 2 and get -7.
We add -7 to 10 and get 3 as the next digit of the result.

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

Step 4: We'll start by subtracting the digit 9 and the borrow 0 from 2 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 3 and the borrow 1 from 8 in column 5 and get 4.
4 is the next digit of our result.

So, 82426 - 39095 = 43331.