You can solve this problem in pure algebraic way counting atoms.

a(2N) + b(2H) = c(N+3H)

You should solve the problem in integers.

Putting tentatively a=1 we have 2=c and 2b=3c from which b=3.

Finally chemical equation (in molecules) should be:

N2 + 3H2 = 2NH3

or analogously:

putting b=1 we have 2=3c => c=2/3 and a=1/3

(1/3)N2 + H2 = (2/3)NH3

and finally

N2 + 3H2 = 2NH3

and so on