Okay, we are tasked with adding 9004 and 581. Let's begin!

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

Step 2: We'll start by adding the digits 0 & 8 in column 2 and get 8.

Step 3: We'll start by adding the digits 0 & 5 in column 3 and get 5.

Step 4: We'll start by adding the digits 9 & 0 in column 4 and get 9.

So, 9004 + 581 = 9585.

