Okay, let's tackle this math problem. We're starting with 423206 and subtracting 67519.

Step 1: We'll start by subtracting the digit 9 and the borrow 0 from 6 in column 1 and get -3.
We add -3 to 10 and get 7 as the first digit of the result.

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

Step 3: We'll start by subtracting the digit 5 and the borrow 1 from 2 in column 3 and get -4.
We add -4 to 10 and get 6 as the next digit of the result.

Step 4: We'll start by subtracting the digit 7 and the borrow 1 from 3 in column 4 and get -5.
We add -5 to 10 and get 5 as the next digit of the result.

Step 5: We'll start by subtracting the digit 6 and the borrow 1 from 2 in column 5 and get -5.
We add -5 to 10 and get 5 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, 423206 - 67519 = 355687.