Alright, let's solve this problem step by step. We have 9094 and 577 and we're adding them together.

Step 1: We'll start by adding the digits 4 & 7 in column 1 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 9 & 7 in column 2 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 0 & 5 in column 3 and get 6.

Step 4: We'll start by adding the digits 9 & 0 in column 4 and get 9.

So, 9094 + 577 = 9671.

