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Detection of hidden explosives is of utmost importance for homeland security. Several configurations of an Explosives Detection System (EDS) to intercept hidden threats, made up with a Deuterium-Deuterium (D-D) compact neutron generator and NaI (Tl) scintillation detectors, have been evaluated using MCNP6 code. The system's response to various samples of explosives, such as RDX and Ammonium Nitrate, is analysed. The D-D generator is able to produce fast neutrons with 2.5 MeV energy in a maximum yield of 1010 n/s. It is surrounded by high-density polyethylene to thermalize the fast neutrons and to optimize interactions with the sample inspected, whose emission of gamma rays gives a characteristic spectrum of the elements that constitute it. This procedure allows to determine its chemical composition and to identify the type of substance. The necessary shielding is evaluated to estimate its thicknesses depending on the admissible dose of operation, using lead and polyethylene. The results show that its functionality is promising in the field of national security for explosives inspection.