Alright, let's solve this problem step by step. We have 3741 and 6871 and we're adding them together.

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

Step 2: We'll start by adding the digits 4 & 7 in column 2 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 7 & 8 in column 3 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 3 & 6 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 3741 + 6871 = 10612.

