Okay, we are tasked with adding 4951 and 4566. 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 5 & 6 in column 2 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 9 & 5 in column 3 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

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

So, 4951 + 4566 = 9517.

