解:$\frac {1}{2}x - 2(x - \frac {1}{3}y^2)+(-\frac {3}{2}x + \frac {1}{3}y^2)$
$ =\frac {1}{2}x - 2x+\frac {2}{3}y^2-\frac {3}{2}x + \frac {1}{3}y^2$
$ =(\frac {1}{2}x - 2x-\frac {3}{2}x)+(\frac {2}{3}y^2+\frac {1}{3}y^2)$
$ =-3x + y^2$
$ $当$x = - 2,$$y = \frac {2}{3}$时,
$ $原式$=(-3)×(-2)+(\frac {2}{3})^2$
$ =6+\frac {4}{9}$
$ =6\frac {4}{9}$