Okay, we are tasked with adding 5641 and 3361. Let's begin!

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 4 & 6 in column 2 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 6 & 3 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 5 & 3 in column 4 and get 9.

So, 5641 + 3361 = 9002.

