Okay, we are tasked with adding 1181 and 4415. Let's begin!

Step 1: We'll start by adding the digits 1 & 5 in column 1 and get 6.

Step 2: We'll start by adding the digits 8 & 1 in column 2 and get 9.

Step 3: We'll start by adding the digits 1 & 4 in column 3 and get 5.

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

So, 1181 + 4415 = 5596.

