Alright, let's solve this problem step by step. We have 9433 and 9004 and we're adding them together.

Step 1: We'll start by adding the digits 3 & 4 in column 1 and get 7.

Step 2: We'll start by adding the digits 3 & 0 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 9 & 9 in column 4 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

So, 9433 + 9004 = 18437.

