Alright, let's solve this problem step by step. We have 3977 and 7907 and we're adding them together.

Step 1: We'll start by adding the digits 7 & 7 in column 1 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 0 in column 2 and get 8.

Step 3: We'll start by adding the digits 9 & 9 in column 3 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 3 & 7 in column 4 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

So, 3977 + 7907 = 11884.

