A girl is standing facing towards the south. She turns $135^{\circ }$ in the anticlockwise direction and then again takes a $180^{\circ }$ turn in the anticlockwise direction. Which direction is she facing now?

Let's calculate the total effective turn in the anticlockwise direction:
$$\text{Total anticlockwise turn}=135^{\circ }+180^{\circ }=315^{\circ }$$
Turning $315^{\circ }$ anticlockwise is equivalent to turning clockwise by:
$$360^{\circ }-315^{\circ }=45^{\circ }\text{ clockwise}$$
Initial direction = SouthTurning $45^{\circ }$ clockwise from South moves her towards the South-west direction.