Let's solve this addition problem. We have 4638 and 5039, 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 3 & 3 in column 2 and get 7.

Step 3: We'll start by adding the digits 6 & 0 in column 3 and get 6.

Step 4: We'll start by adding the digits 4 & 5 in column 4 and get 9.

So, 4638 + 5039 = 9677.

