Okay, we are tasked with adding 4401 and 1278. Let's begin!

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

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 4 & 2 in column 3 and get 6.

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

So, 4401 + 1278 = 5679.

