Alright, let's solve this problem step by step. We have 7641 and 2183 and we're adding them together.

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

Step 2: We'll start by adding the digits 4 & 8 in column 2 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 6 & 1 in column 3 and get 8.

Step 4: We'll start by adding the digits 7 & 2 in column 4 and get 9.

So, 7641 + 2183 = 9824.

