How to tell the difference between resistors in series and in parallel?
Your attempt at part(a) is correct.

How can I identify if two components are in parallel or in serial configuration?

If the same current is flowing through both of the components. Then they are in series. 

If a current is split up between both of the components and then joined back together. Then they are in parallel.



Let's look at 2Ω and 6Ω. Does the same current that goes through the 2Ω also go through the 6Ω? Yes. Then they are in series. 

Does the current that goes through 2Ω also go through the 3Ω? No, however the current from 2Ω and 3Ω is split where they meet.

Does the current that goes through the 2Ω also go through the 5Ω? No.

Does the current that goes through 6Ω also go through 5Ω? No, however their current is joined.

Does the current that goes through 3Ω also go through 5Ω? Yes. Then they are in series. 



Resistors that are in series can be summed to make larger resistors. 

The 2Ω and 6Ω were in series, let's sum them into 8Ω.

The 3Ω and 5Ω were in series, let's sum them into 8Ω. 

And as before we noticed that the current was split at one point, and then joined back together. So the 8Ω is in parallel with the other 8Ω. 

And like you calculated, you'll get 4Ω which is the correct answer.