Okay, we are tasked with adding 7742 and 8133. Let's begin!

Step 1: We'll start by adding the digits 2 & 3 in column 1 and get 5.

Step 2: We'll start by adding the digits 4 & 3 in column 2 and get 7.

Step 3: We'll start by adding the digits 7 & 1 in column 3 and get 8.

Step 4: We'll start by adding the digits 7 & 8 in column 4 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

So, 7742 + 8133 = 15875.

