Let's dive into this subtraction. We'll start with 206584 and subtract 53419 from it.

Step 1: We'll start by subtracting the digit 9 and the borrow 0 from 4 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 1 and the borrow 1 from 8 in column 2 and get 6.
6 is the next digit of our result.

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

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

Step 5: We'll start by subtracting the digit 5 and the borrow 0 from 0 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 2 in column 6 and get 1.
1 is the next digit of our result.

So, 206584 - 53419 = 153165.