Strike rotation during a six

No, The strike can only be rotated it the batsman actually run between the wickets thats what they only rotate strike for the ODD number of runs made, 6 is an even number so the batsman who hit the run remains on the strike.

The situation is different if the batsmen hits a six on the last of the over, then indefinitely the batsmen men have to change the strike due to the completion of the over

"Switching of batting and bowling ends after every over is done to make the game fair and reduce any advantage due to external factors such as:

Wind direction (which might support the batsman or the bowler) Ground dimensions (the ground might have certain boundaries shorter or longer than the others) Pitch conditions (batting continuously on one side might degrade the pitch from that end; one side might have more spin or bounce than the other)" In which the batsman doesn’t change the side the bowler does.