Okay, we are tasked with adding 5101 and 4676. Let's begin!

Step 1: We'll start by adding the digits 1 & 6 in column 1 and get 7.

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 1 & 6 in column 3 and get 7.

Step 4: We'll start by adding the digits 5 & 4 in column 4 and get 9.

So, 5101 + 4676 = 9777.

