Alright, let's solve this problem step by step. We have 7708 and 4511 and we're adding them together.

Step 1: We'll start by adding the digits 8 & 1 in column 1 and get 9.

Step 2: We'll start by adding the digits 0 & 1 in column 2 and get 1.

Step 3: We'll start by adding the digits 7 & 5 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 7 & 4 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 7708 + 4511 = 12219.

