Alright, let's solve this problem step by step. We have 6179 and 2590 and we're adding them together.

Step 1: We'll start by adding the digits 9 & 0 in column 1 and get 9.

Step 2: We'll start by adding the digits 7 & 9 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 1 & 5 in column 3 and get 7.

Step 4: We'll start by adding the digits 6 & 2 in column 4 and get 8.

So, 6179 + 2590 = 8769.

