The position of the points $\left(-1,2\right),\left(2,-3\right)$  with respect to the line $2x-3y+1=0$  are

$\left(x_1,y_1\right)=\left(-1,2\right)$

$\left(x_2,y_2\right)=\left(2,3\right)$

$L_{11}=2\left(-1\right)-3\left(2\right)+1=-2-6+1=-7<0$

$L_{22}=2\left(2\right)-3\left(-3\right)+1=4+9+1=14>0$

$\therefore$ $L_{11}\&L_{22}$  have opposite sign

$\therefore$ $\left(-1,2\right)\left(2,-3\right)$  are opposite side of the line $L=0$