We can solve this together! We're beginning with 666082 and removing 84890 from it.

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

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

Step 3: We'll start by subtracting the digit 8 and the borrow 1 from 0 in column 3 and get -9.
We add -9 to 10 and get 1 as the next digit of the result.

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

Step 5: We'll start by subtracting the digit 8 and the borrow 0 from 6 in column 5 and get -2.
We add -2 to 10 and get 8 as the next digit of the result.

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

So, 666082 - 84890 = 581192.