Okay, we are tasked with adding 2007 and 582. Let's begin!

Step 1: We'll start by adding the digits 7 & 2 in column 1 and get 9.

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 2 & 0 in column 4 and get 2.

So, 2007 + 582 = 2589.

