Will had two less than three times as many video games as Josh.
If Will has 20, how many does Josh have?
Three times the number of video games Josh has is 20+2 = <<3*20+2=62>>62
Two less than three times as many video games as Josh has is 62-2 = <<62-2=60>>60
Josh has <<60=60>>60 video games. Answer: \boxed{60}.