Alright, let's solve this problem step by step. We have 7763 and 4004 and we're adding them together.

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 & 0 in column 2 and get 6.

Step 3: We'll start by adding the digits 7 & 0 in column 3 and get 7.

Step 4: We'll start by adding the digits 7 & 4 in column 4 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

So, 7763 + 4004 = 11767.

