Let's break this down. We're going to add 1004 and 4148 together.

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

Step 2: We'll start by adding the digits 0 & 4 in column 2 and get 5.

Step 3: We'll start by adding the digits 0 & 1 in column 3 and get 1.

Step 4: We'll start by adding the digits 1 & 4 in column 4 and get 5.

So, 1004 + 4148 = 5152.

