how would I expand the 4 bit full adder when it only has the Carry Out and 4 sum outputs?

How does the 4-bit full adder work? It uses multiple 1-bit full adders and combines them. Use the same idea to use two 4-bit adders and combine them to make an 8-bit adder.

 

It's something that we are given alot of time to figure out and complete, therefore expecting us to work through it and figure it out. But I am at a standstill

This is because the approach that you seem to be taking is to avoid understanding the problem or decomposing into a set of smaller, simpler problems and, instead, ask strangers to spoon feed you a solution. You need to get over that approach because you are studying engineering and engineers, pretty much by design, are the people that solve other peoples' problems. The digital logic is a small part of this project -- the main thing your instructor is wanting you to learn is how to solve engineering problems.

 

This is because the approach that you seem to be taking is to avoid understanding the problem or decomposing into a set of smaller, simpler problems and, instead, ask strangers to spoon feed you a solution. You need to get over that approach because you are studying engineering and engineers, pretty much by design, are the people that solve other peoples' problems. The digital logic is a small part of this project -- the main thing your instructor is wanting you to learn is how to solve engineering problems.

I am not asking you or anyone else to spoon feed me the answer, just looking for advice on how to go about this. I appreciate your passion for this but this class is not related to my field of study. Its just a filler class

 

I am not asking you or anyone else to spoon feed me the answer, just looking for advice on how to go about this. I appreciate your passion for this but this class is not related to my field of study. Its just a filler class

And yet you haven't offered up any attempt at a solution, but instead keep asking for people to tell you how to do it.

This may be a "filler class" in your mind, but it's (most likely) designed as a majors course and so, whether it is related to your field or not, if you take the course, you are expected to put in the effort associated with a majors course.

You've been given a number of hints and suggestions. Use them to come up with your best attempt and post that. We are then in a position to help you better understand where and why you have issues and guide you toward ways to overcome them.