Okay, we are tasked with adding 2774 and 4003. Let's begin!

Step 1: We'll start by adding the digits 4 & 3 in column 1 and get 7.

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

Step 3: We'll start by adding the digits 7 & 0 in column 3 and get 7.

Step 4: We'll start by adding the digits 2 & 4 in column 4 and get 6.

So, 2774 + 4003 = 6777.

