Let's solve this addition problem. We have 8644 and 5074, and we need to add them together.

Step 1: We'll start by adding the digits 4 & 4 in column 1 and get 8.

Step 2: We'll start by adding the digits 4 & 7 in column 2 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 6 & 0 in column 3 and get 7.

Step 4: We'll start by adding the digits 8 & 5 in column 4 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

So, 8644 + 5074 = 13718.

