We work out (i) the number of moles of #N_2O_4#, and (ii) convert this to molecules.
Explanation:
#"Moles of dinitrogen tetroxide"##=##(76.3*g)/(92.011*g*mol^-1)#. This gives an answer in #"moles"#. Now it is a fact that in #1##"mole"# of stuff there are #6.022xx10^23# individual items of that stuff:
#"Number of "N_2O_4" molecules"##=##6.022xx10^23mol^-1xx(76.3*g)/(92.011*g*mol^-1)##=##??" molecules."#