Alright, let's solve this problem step by step. We have 585683 and 42065, and we're subtracting the second number from the first.

Step 1: We'll start by subtracting the digit 5 and the borrow 0 from 3 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 6 and the borrow 1 from 8 in column 2 and get 1.
1 is the next digit of our result.

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

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

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

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

So, 585683 - 42065 = 543618.