A product of numbers is 0 only if at least one number is 0. cos(x) is 0 when x is an odd multiple of [itex]\pi/2[/itex]. For what values of t is 192t an odd integer? For what values of t is 8t an odd integer?
I have no idea what you are doing! I get 192/2= 96 values of t so that 192t is an odd integer (so that [itex]cos(96\pi t)= 0[/itex]) and 8/2= 4 values of t so that 8t is an odd integer (and [itex]cos(4\pi t)= 0[/itex]). That gives a total of 90 values of t for which [itex]cos(96\pi t)cos(4\pi t)= 0[/itex].
You are looking for t such that 192t is an odd integer. 192t= 1 if t= 1/192, of course, but also, 192t= 3 if t= 3/192, 192t= 5 if t= 5/192, etc. We can do that for every odd integer up to 192- and 192/2 of the integers less than 192 are odd.