Okay, we are tasked with adding 6319 and 5919. Let's begin!

Step 1: We'll start by adding the digits 9 & 9 in column 1 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 1 & 1 in column 2 and get 3.

Step 3: We'll start by adding the digits 3 & 9 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 6 & 5 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 6319 + 5919 = 12238.

