We can solve this together! We're beginning with 843203 and removing 35586 from it.

Step 1: We'll start by subtracting the digit 6 and the borrow 0 from 3 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 8 and the borrow 1 from 0 in column 2 and get -9.
We add -9 to 10 and get 1 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 5 and the borrow 1 from 3 in column 4 and get -3.
We add -3 to 10 and get 7 as the next digit of the result.

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

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

So, 843203 - 35586 = 807617.