This study contains the solution of the dark matter mystery of spiral galaxies by using the space of four distance dimensions x, y, z, x', in which x' is the fourth distance dimension. The calculation of galaxy rotation has been presented in the space of four dimensions by using two dimensional section x, x' and three dimensional section x, y, x'. The four dimensional mass M which generates the main gravitation field of galaxy is located at the fourth dimension at the distance x' = X' and other dimensions are zero x = 0, y = 0, z = 0. The method to calculate the speed distribution curve of four dimensional mass VM: the speed distribution curve VM is calculated by using the equation in which the gravitational force is equal to the centrifugal force of rotation. The solution of this equation yields the speed distribution component VM of the four dimensional mass M and the value of the mass M. In the publication [1] has been presented rotational speed distributions curves of the galaxy NGC 3198. The speed distribution curve of galactic halo in that publication corresponds to the speed distribution curve VM of four dimensional mass M of this study. In order to find out how well this four dimensional model functions, the speed distribution curve VM of four dimensional mass M has been calculated by using two pairs of rotational radius and speed values. The conclusions and findings: the calculated distribution curve VM was a good match for the halo curve of the publication [1]. Furthermore, four rotational speed distribution curve VM was calculated using different values of the distance X', which yielded different values for the maximum radius of galaxy. In this manner the different galaxy models of the publication [2] were obtained. By that means the solution of dark matter mystery has been proved.