Question

I still don't understand how to solve those kind of Geometry thing so please explain and show your work.

Answer 1

Alternate means they are on opposite sides of the transversal... 
Same side means they are on the same side of the transversal..
interior mean they are inside the parallel lines
exterior means they are on the outside of parallel lines.

If you have two parallel lines cut by a transversal there you know that the angles are either going to be supplementary or they are going to be congruent. Those are your only two choices.  Now you just have to decide which is which.

FEG and CBE are indeed supplementary but they don't have a relationship
CBE and DEB are same side interior angles because they are on the same side of the transversal and inside the parallel lines
Answer C is exactly what I said above, they just label B wrong to trick you
FEG and DEB are vertical angles because they are formed by the intersection of two lines and are non adjacent

So answer C would be correct