Alright, let's solve this problem step by step. We have 4623 and 4171 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 2 & 7 in column 2 and get 9.

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 4 & 4 in column 4 and get 8.

So, 4623 + 4171 = 8794.

