Okay, we are tasked with adding 7644 and 1747. Let's begin!

Step 1: We'll start by adding the digits 4 & 7 in column 1 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 4 & 4 in column 2 and get 9.

Step 3: We'll start by adding the digits 6 & 7 in column 3 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 7 & 1 in column 4 and get 9.

So, 7644 + 1747 = 9391.

