Okay, we are tasked with adding 4504 and 4074. Let's begin!

Step 1: We'll start by adding the digits 4 & 4 in column 1 and get 8.

Step 2: We'll start by adding the digits 0 & 7 in column 2 and get 7.

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

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

So, 4504 + 4074 = 8578.

