Alright, lets get started.
Zach has 3/4 hour to play video games.
Lets converts it into minutes. 
 means
 means 
 minutes.
 minutes.
It takes him 1/12 hour to set up the system means he has 
 minutes to set up the system.
 minutes to set up the system.
So, he has left time for playing = 
 minutes
 minutes
Each round of his favorite game takes 1/6 hour means 
 minutes for each round.
 minutes for each round.
It means he has 40 minutes for playing and each round takes 10 minutes.
So, number of rounds he can play= 

He can play 4 rounds of his favorite game. : Answer
Hope it will help :)