Okay, we are given 6563 and 3674. Let's add them up step by step.

Step 1: We'll start by adding the digits 3 & 4 in column 1 and get 7.

Step 2: We'll start by adding the digits 6 & 7 in column 2 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 5 & 6 in column 3 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 6 & 3 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 6563 + 3674 = 10237.

