Okay, we are tasked with adding 4442 and 5561. Let's begin!

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

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 4 & 5 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 4 & 5 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 4442 + 5561 = 10003.

