Alright, let's solve this problem step by step. We have 8204 and 7435 and we're adding them together.

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 2 & 4 in column 3 and get 6.

Step 4: We'll start by adding the digits 8 & 7 in column 4 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

So, 8204 + 7435 = 15639.

