Okay, we are tasked with adding 4679 and 6066. Let's begin!

Step 1: We'll start by adding the digits 9 & 6 in column 1 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 6 in column 2 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 6 & 0 in column 3 and get 7.

Step 4: We'll start by adding the digits 4 & 6 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 4679 + 6066 = 10745.

