Alright, let's solve this problem step by step. We have 8631 and 1144 and we're adding them together.

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

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

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

Step 4: We'll start by adding the digits 8 & 1 in column 4 and get 9.

So, 8631 + 1144 = 9775.

