Designing two stage CE amplifier with negative feedback
Steps to solve this:

Draw the small signal equivalent circuit. From that you can derive the small signal parameters \$R_{in}\$, \$R_{out}\$ and the gain over frequency. \$R_{in}\$ and \$R_{out}\$ might depend on the \$gm\$ of the transistors so \$R_{in}\$ and \$R_{out}\$ will be expressed as the gm of one or more transistors and values of resistors.

This circuit has feedback which complicates things. You should know that circuits with feedback have a transfer of \$A/(1+A\beta)\$. You can just open the loop and then evaluate A and \$\beta\$ separately.

Then also realize what the relations are between the open loop \$R_{out}\$ and the closed loop \$R_{out}\$. Generally Rout will become much lower in closed loop (as the circuit "counteracts" any changes at the output).

Determine what components affect the behavior over frequency so look for RC time constants in the circuit, C1 and R6 is an example. Think what influence this RC circuit has (C1 shorts R6 at high frequencies) and what the crossover frequency of that RC is.

Yep, this is not easy! The steps should really have been explained in a course, book or class as this is not something you can figure out yourself. The question rises why a "Noobie" like yourself has to be able to solve this. It is not like you are ever going to need this unless you want to become a Analog circuit designer. And then you would have chosen to learn this yourself.

Oh, and this is not "designing"! This is dimensioning meaning, the circuit is there and you can only play with the component values. Also, I guess that even many Electrical Engineers with a Master's in Electrical Engineering would have a hard time to dimension this circuit properly. Most would just use a circuit simulator. Personally I would do the same but as I have a lot of experience (more than 25 years) in Analog design I can start with better initial values for the resistors and I also know what the effect is of changing certain (combinations of) resistors. So if for example the gain is too low, I immediately know what my options are to solve that. As a newbie, you lack that experience so you have to do this the hard way.