Okay, let's tackle this math problem. We're starting with 584331 and subtracting 42499.

Step 1: We'll start by subtracting the digit 9 and the borrow 0 from 1 in column 1 and get -8.
We add -8 to 10 and get 2 as the first digit of the result.

Step 2: We'll start by subtracting the digit 9 and the borrow 1 from 3 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 4 and the borrow 1 from 3 in column 3 and get -2.
We add -2 to 10 and get 8 as the next digit of the result.

Step 4: We'll start by subtracting the digit 2 and the borrow 1 from 4 in column 4 and get 1.
1 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, 584331 - 42499 = 541832.