Okay, we are tasked with adding 4770 and 742. Let's begin!

Step 1: We'll start by adding the digits 0 & 2 in column 1 and get 2.

Step 2: We'll start by adding the digits 7 & 4 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 7 & 7 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 & 0 in column 4 and get 5.

So, 4770 + 742 = 5512.

