To find the number of molecules in 68.0g N2 you start by finding the number of moles then convert moles to molecules.
The first step is divide the grams by the molar mass of N2,
which is 2(14.01) g/mol:
68.0g x (1 mol/28.02g) = 2.43 moles of N2
Now multiply the moles of N2 by Avogadro's number, the number of particles in a mole:
2.43 mol N2 x 6.02 x 10^23 molecules/mol = 1.46 x 10^24 molecules of N2
Include the units with the conversion factors (molar mass and Avogadro's number). Proper canceling of units will give you the units of molecules for the answer, which is an indication that you set the problem up correctly.