Okay, we are tasked with adding 5151 and 6187. Let's begin!

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

Step 2: We'll start by adding the digits 5 & 8 in column 2 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

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

Step 4: We'll start by adding the digits 5 & 6 in column 4 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

So, 5151 + 6187 = 11338.

