Let's solve this addition problem. We have 1777 and 5186, and we need to add them together.

Step 1: We'll start by adding the digits 7 & 6 in column 1 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 8 in column 2 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 7 & 1 in column 3 and get 9.

Step 4: We'll start by adding the digits 1 & 5 in column 4 and get 6.

So, 1777 + 5186 = 6963.

