Okay, we are tasked with adding 1333 and 4167. Let's begin!

Step 1: We'll start by adding the digits 3 & 7 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 3 & 6 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 3 & 1 in column 3 and get 5.

Step 4: We'll start by adding the digits 1 & 4 in column 4 and get 5.

So, 1333 + 4167 = 5500.

