Okay, we are tasked with adding 7594 and 7113. Let's begin!

Step 1: We'll start by adding the digits 4 & 3 in column 1 and get 7.

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 & 1 in column 3 and get 7.

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

So, 7594 + 7113 = 14707.

