This work reports results of two different measurements of resonant elastic scattering 20^Ne(4^He, 4^He)20^Ne on a thick 4^He gas target. The parameters of the experimental setup were adjusted to investigate the astrophysically relevant range of excitation energies of the 24^Mg nucleus. From the detected 4^He experimental data, excitation energy spectra were calculated for each measurement, which were then normalized to see the representation of a particular recognized resonance state in the spectrum. The detected resonance states of both measurements were compared. Obtained results are in agreement with availible experimental results. A total of 19 different resonance states were observed in the 24^Mg nucleus in the astrophysically relevant energy range 12.50 MeV - 18.50 MeV. In the second part of the work, Monte-Carlo simulations were used to determine the parameters of a new experimental setup in which 24^Mg would be synthesized by the same input nuclear reaction in the astrophysically relevant range of excitation energies. Decay of 24^Mg would be studied again, this time in coincident measurement which enables identification of the decay channel. The setup is designed to detect in coincidance the decay products of the channels: 12^C + 12^C, 20^Ne + 4^He and 20^Ne∗ + 4^He.