Answer: 6.75 moles of hydrogen gas are produced.
Step-by-step explanation:
According to the law of conservation of mass, mass can neither be created nor be destroyed. Thus the mass of products has to be equal to the mass of reactants. The number of atoms of each element has to be same on reactant and product side. Thus chemical equations are balanced.
The decomposition of ammonia is shown as:

According to stoichiometry:
2 moles of ammonia decompose to produce = 3 moles of hydrogen
Thus 4.5 moles of ammonia decompose to produce =
moles of hydrogen
Thus 6.75 moles of hydrogen are produced.