Let us assume that direction towards the east is positive x-axis and towards the west is negative x-axis.

The direction towards the north is positive y-axis and towards the south is negative y-axis.

Let initial point is A and final point is B.

Now total displacement AB = -4i + 3(i*sin30 + j*cos30)

                                         = -4i + 3(i*1/2 + j*√3/2 )

                                         = -4i + i*3/2 + j*3√3/2 

                                         =  -i*5/2 + j*3√3/2 

Now |AB| = √{(5/2)2 + (3√3/2)2}

               = √(25/4 + 27/4)

               = √52/4

               = √13 km

So the girl displacement from her initial point of departure √13 km