Okay, we are given 6624 and 5113. Let's add them up step by step.

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

Step 2: We'll start by adding the digits 2 & 1 in column 2 and get 3.

Step 3: We'll start by adding the digits 6 & 1 in column 3 and get 7.

Step 4: We'll start by adding the digits 6 & 5 in column 4 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

So, 6624 + 5113 = 11737.

