The particle has 4J of potential energy at x = 2m (read from the graph). As the particle moves from x = 2 m to x = 4 m , it is losing kinetic energy and gaining potential energy. Since the total mechanical energy is constant, (mechanical energy = sum of kinetic + potential energy), the particle would need to have 8J of energy to reach x = 4 m. This would occur when the potential energy = 8 J and kinetic energy = 0 J. If the particle has more potential energy than 8J, it could easily make it to x = 6 m. Therefore, our maximum mechanical energy is 8 J.
Returning to x = 2 m, if the mechanical energy = 8 J and the potential energy = 4 J, that must mean that the kinetic energy is equal to 4 J. The velocity can be calculated by setting 1/2mv^2 = 8 J, and substituting m = 0.280 kg, giving v = 5.35 m/s.