Okay, we are tasked with adding 259 and 6341. Let's begin!

Step 1: We'll start by adding the digits 9 & 1 in column 1 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 5 & 4 in column 2 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 2 & 3 in column 3 and get 6.

Step 4: We'll start by adding the digits 0 & 6 in column 4 and get 6.

So, 259 + 6341 = 6600.

