Alright, let's solve this problem step by step. We have 2563 and 4081 and we're adding them together.

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

Step 2: We'll start by adding the digits 6 & 8 in column 2 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 5 & 0 in column 3 and get 6.

Step 4: We'll start by adding the digits 2 & 4 in column 4 and get 6.

So, 2563 + 4081 = 6644.

