Okay, we are tasked with adding 4328 and 4513. Let's begin!

Step 1: We'll start by adding the digits 8 & 3 in column 1 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 2 & 1 in column 2 and get 4.

Step 3: We'll start by adding the digits 3 & 5 in column 3 and get 8.

Step 4: We'll start by adding the digits 4 & 4 in column 4 and get 8.

So, 4328 + 4513 = 8841.

