Pros/Cons of different Exhaust types

I've been trying to find a decent answer to the differences between X/Y/H Pipes. Could anyone please give me a good explanation considering I know nothing about mechanics?

I bought mine used and it's a 2005 V6 with dual exhaust. Single Muffler on the right side. Any ideas what this could be? (images attached)



Thanks guys,

Thanks Dave,

I'll try to get a pic of the underbelly