Okay, we are tasked with adding 4005 and 4642. Let's begin!

Step 1: We'll start by adding the digits 5 & 2 in column 1 and get 7.

Step 2: We'll start by adding the digits 0 & 4 in column 2 and get 4.

Step 3: We'll start by adding the digits 0 & 6 in column 3 and get 6.

Step 4: We'll start by adding the digits 4 & 4 in column 4 and get 8.

So, 4005 + 4642 = 8647.

