Figure-8 trajectories have been crucial paths especially for manned Moon missions. Figure-8 trajectories, also called free return trajectories, as their names refer, are 8-shaped trajectories, in which an object returns with no fuel requirement once it is inserted. In Apollo-13 Mission, two days after the launch, during the coast to the Moon, an oxygen tank exploded and the mission canceled. The only chance for the astronauts to return Earth was free return path. In this paper, the trajectory followed in this dramatic event is studied. In order to find the figure-8 free return trajectory, three solution methods are applied: Lunar patched conic approach, numerical integration of the motion of equations, and restricted three-body problem approach. Starting from the actual Apollo-13 flight parameters at Lunar injection point, the solution methods are used in order to be inserted into the same trajectory with the mission. Comparing the results, advantages and disadvantages of each method are analyzed. In addition, effects of the Sun's and other planets' gravitational attraction on the trajectory have been studied. As a result, the Lunar patched conic approximation is found to be applicable only to get the initial estimates of the initial conditions. The numerical method, though the heavy computational cost, fits with the problem and provides the desired parameters accurately considering the perturbative effects. Finally, the restricted three-body problem approach provides very precise results neglecting the effects of the Sun; however, the Sun affects the trajectory dramatically.