Alright, let's solve this problem step by step. We have 6417 and 4621 and we're adding them together.

Step 1: We'll start by adding the digits 7 & 1 in column 1 and get 8.

Step 2: We'll start by adding the digits 1 & 2 in column 2 and get 3.

Step 3: We'll start by adding the digits 4 & 6 in column 3 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 6 & 4 in column 4 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

So, 6417 + 4621 = 11038.

