Why does the field at the centre of currnt carrying coil is in clokwise and anticlockwise direction

Question is not correct.

 

Magnetic field due to the current carrying coil is either coming towards the observer or going away from observer

depends on the current direction in the coil if the coil is held vertically. 

 

As shown in figure if current is in anticlockwise direction and the cuurent carrying coil 

is in the plane of figure, then magnetic field direction is going into the plane of figure.

 

 if current is in clockwise direction and the cuurent carrying coil 

is in the plane of figure, then magnetic field direction is coming out from the plane of figure.