Alright, let's solve this problem step by step. We have 1970 and 7777 and we're adding them together.

Step 1: We'll start by adding the digits 0 & 7 in column 1 and get 7.

Step 2: We'll start by adding the digits 7 & 7 in column 2 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 9 & 7 in column 3 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 1 & 7 in column 4 and get 9.

So, 1970 + 7777 = 9747.

