Okay, we are tasked with adding 6519 and 3145. Let's begin!

Step 1: We'll start by adding the digits 9 & 5 in column 1 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 1 & 4 in column 2 and get 6.

Step 3: We'll start by adding the digits 5 & 1 in column 3 and get 6.

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

So, 6519 + 3145 = 9664.

