Okay, we are tasked with adding 2597 and 1699. Let's begin!

Step 1: We'll start by adding the digits 7 & 9 in column 1 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 9 & 9 in column 2 and get 19.
We'll write down the last digit 9 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 5 & 6 in column 3 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 2 & 1 in column 4 and get 4.

So, 2597 + 1699 = 4296.

