To solve the centers on the 4x4 Supercube first twist pairs of centers to get them all pointing in the same direction on each face using the method shown below and then complete the solve by using the 3x3 Supercube Sequences to twist four centers (as one) on pairs of faces.

The following two sequences are used together to fix centers on the supercube. They are the same except that the sequence on the first cube twists both slices between the front and back layers whereas the sequence on the second cube only twists one slice.

The following shows how the above two sequences are combined to twist two centers (on front face) that are pointing in opposite directions so they point in the same direction. There is a half twist of the top face between the sequences and another at the end. This method also results in all four centers on the top face being twisted but that does not matter because at this point the goal is just to get all centers pointing in the same direction on each face.

To use the above sequence it is only necessary that there are two centers with arrows pointing in opposite directions in the locations shown on the front face. The direction of the arrows does not have to match the above cube nor do the rest of the arrows on the face. The result will be that the two arrows point in the same direction but not necessarily in the same direction as the rest of the arrows on the face (if the other two centers already point in the same direction then all four centers will point in the same direction after doing the sequence but they still may not match the rest of the face).

The following shows how the above sequence is used to get all centers pointing in the same direction on each face. In the table below the cube, "Make Setup" means to turn the cube so that there are two centers with arrows pointing in opposite directions in the locations shown on the above cube.

Complete the solve by using the 3x3 sequences. Turn the cube so both the front and top faces have centers that need to be half-twisted and then apply the sequence to fix them as shown (moves 1-10). Then turn the cube so the remaining unsolved centers are on the front & top faces, and apply the sequence to quarter-twist the front counter-clockwise and the top clockwise (11-20) which will fix the front but not the top. The centers on the top face are now half-twisted so fix those with the sequence that twists the top face only as shown (21-32). The last move turns the cube to the home position (all arrows point up).

You can try using the above sequences to solve 4x4 Supercubes With Random Centers.