Okay, we are tasked with adding 4641 and 4500. Let's begin!

Step 1: We'll start by adding the digits 1 & 0 in column 1 and get 1.

Step 2: We'll start by adding the digits 4 & 0 in column 2 and get 4.

Step 3: We'll start by adding the digits 6 & 5 in column 3 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

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

So, 4641 + 4500 = 9141.

