If 6 liters of hydrogen gas are used, how many liters of nitrogen gas will be needed for the above reaction at stp?

Are you referring to this reaction?  
N2 + 3H2 --> 2NH3 

If so, then let us work it out.

6 liters of H2 at STP is: We will be using stochiometry on the equation, therefore, in ever 3mol of H2 that you react, you have to react 1 mol of N2 too.

6L (1000mL/L) ( cm^3/mL) (m/100cm)^3 ( .0899kg/m^3 )(1000g/kg) (1mol/ 2.016g)

 = .2678mols of H2. 

So,
.2678mols of H2 ( 1mol N2 / 3mols of H2)  is  .08927 mols N2 

Then, by using the properties of nitrogen,  continue working it out by doing the same conversion backwards:
.08927mols x 28.02 g/mol x kg/1000g x 1m^3 / 1.2506kg x (100cm/m)^3 x mL/cm^3 x L/1000mL = 2L 

Therefore,  2 Liters is required for the reaction above.

4d^55s^1 ( third choice)