Okay, we are given 4374 and 9409. Let's add them up step by step.

Step 1: We'll start by adding the digits 4 & 9 in column 1 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 0 in column 2 and get 8.

Step 3: We'll start by adding the digits 3 & 4 in column 3 and get 7.

Step 4: We'll start by adding the digits 4 & 9 in column 4 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

So, 4374 + 9409 = 13783.

