Alright, let's solve this problem step by step. We have 6594 and 3910 and we're adding them together.

Step 1: We'll start by adding the digits 4 & 0 in column 1 and get 4.

Step 2: We'll start by adding the digits 9 & 1 in column 2 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 5 & 9 in column 3 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 6 & 3 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 6594 + 3910 = 10504.

