Okay, we are tasked with adding 3823 and 5514. Let's begin!

Step 1: We'll start by adding the digits 3 & 4 in column 1 and get 7.

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

Step 3: We'll start by adding the digits 8 & 5 in column 3 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 3 & 5 in column 4 and get 9.

So, 3823 + 5514 = 9337.

