The two X-Center orbits on the 6x6 Cube can be solved separately using the 4x4 sequences. The first cube below shows the quarter-twist sequence for the inner orbit, the second cube shows it for the outer orbit.

The first cube below shows the half-twist sequence for all four X-Centers on the front and top faces in the inner orbit and the second cube shows it for the outer orbit. The sequences can also be used to quarter-twist the centers by altering the right-twist moves (5 & 12), if the first right-twist is clockwise then the second one must be counter-clockwise & vice-versa.

The first cube below shows the half-twist sequence for all four X-Centers on just the top face in the inner orbit and the second cube shows it for the outer orbit.

You can try using the above sequences to solve 6x6 Supercubes With Random X-Centers.