Alright, let's solve this problem step by step. We have 8624 and 6176 and we're adding them together.

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

Step 2: We'll start by adding the digits 2 & 7 in column 2 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 6 & 1 in column 3 and get 8.

Step 4: We'll start by adding the digits 8 & 6 in column 4 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

So, 8624 + 6176 = 14800.

