Let's solve this addition problem. We have 4578 and 4009, and we need to add them together.

Step 1: We'll start by adding the digits 8 & 9 in column 1 and get 17.
We'll write down the last digit 7 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 5 & 0 in column 3 and get 5.

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

So, 4578 + 4009 = 8587.

