During the landing reverse thrust of an aircraft engine is seen that the compressor fan rotates in opposite direction to counter the aircraft's forward motion if I'm right So, my question here is "does the engine stops its rotation(clockwise) and than starts to rotate it in opposite direction(anti-clockwise) So, as to perform the reverse thrust operation?
During the landing reverse thrust of an aircraft engine is seen that the compressor fan rotates in opposite direction
This is wrong
Reverse thrust does not reverse the rotation of the fan/compressor/turbine.
Reverse thrust "simply" redirect the airflow coming out of the turbine in the reverse direction (well, almost, as we'll see in a moment) w.r.t. the usual one.
In the image you posted, the thrust reversers are deployed, and you can see them circled here:
The airflow is the coming out not from the back of the engine, but from the sides, slightly directed forward. The thrust (i.e. the force that the airflow is imposing on the aircraft) is directed backwards, while normally is directed forwards, it is then reversed.
This is nicely illustrated in this image (source)
NOTE: there are different typologies of thrust reversers, this is only one of them, but none of them require spinning the engine in the opposite direction.
When you put your car in reverse gear, does the engine first stop and then start spinning in the opposite direction? No. The engine still keeps on spinning in the same direction, it's some extra gears that cause the output to be in the other direction
Similarly, Reverse thrust is merely a deflection of thrust from the rear to the front. It is done using mechanical levers and gates that redirect the flow of thrust to the opposite direction.
If reversal of turbine's rotation was hypothetically required, the resultant reverse thrust would be produced too late and negligible to be of any use. You can't stop a turbine from a massive RPM to nothing within a few seconds, and then spool it up again in the other direction.