Okay, we are tasked with adding 3497 and 6275. Let's begin!

Step 1: We'll start by adding the digits 7 & 5 in column 1 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 9 & 7 in column 2 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 4 & 2 in column 3 and get 7.

Step 4: We'll start by adding the digits 3 & 6 in column 4 and get 9.

So, 3497 + 6275 = 9772.

