Alright, let's solve this problem step by step. We have 4401 and 431 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 0 & 3 in column 2 and get 3.

Step 3: We'll start by adding the digits 4 & 4 in column 3 and get 8.

Step 4: We'll start by adding the digits 4 & 0 in column 4 and get 4.

So, 4401 + 431 = 4832.

