we know that
1) Zach has [tex]3/4[/tex] hour to play video games
Convert to minutes
[tex]1\ hour=60\ minutes[/tex]
[tex](3/4)*60=45\ minutes[/tex]
2) It takes him [tex]1/12[/tex] hour to set up the system
Convert to minutes
[tex](1/12)*60=5\ minutes[/tex]
3) Find time available to play video games
[tex]45\ minutes-5\ minutes=40\ minutes[/tex]
4) Each round of his favorite game takes [tex]1/6[/tex] hour
Convert to minutes
[tex](1/6)*60=10\ minutes[/tex]
5) Divide the time available to play video games by the time each round of his favorite game
[tex]40/10=4\ round[/tex]
therefore
the answer is
[tex]4\ round[/tex]