Okay, we are tasked with adding 8404 and 2035. Let's begin!

Step 1: We'll start by adding the digits 4 & 5 in column 1 and get 9.

Step 2: We'll start by adding the digits 0 & 3 in column 2 and get 3.

Step 3: We'll start by adding the digits 4 & 0 in column 3 and get 4.

Step 4: We'll start by adding the digits 8 & 2 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 8404 + 2035 = 10439.

