Okay, we are given 6738 and 8908. Let's add them up step by step.

Step 1: We'll start by adding the digits 8 & 8 in column 1 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 3 & 0 in column 2 and get 4.

Step 3: We'll start by adding the digits 7 & 9 in column 3 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 6 & 8 in column 4 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

So, 6738 + 8908 = 15646.

