Alright, let's solve this problem step by step. We have 4116 and 1477 and we're adding them together.

Step 1: We'll start by adding the digits 6 & 7 in column 1 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 1 & 7 in column 2 and get 9.

Step 3: We'll start by adding the digits 1 & 4 in column 3 and get 5.

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

So, 4116 + 1477 = 5593.

