The given line $3x-4y=8$ , the points $\left(2,3\right)\left(-4,5\right)$  are on the

The essential condition for the points on the same side or opposite side of the line is $a{x}_1+b{y}_1+c$  and $a{x}_2+b{y}_2+c$  are  of  same sign, or opposite sign respectively.

Let $ax+by+c_1=0$ , then value of  L₁₁  at $\left(2,3\right)$  is

$\Rightarrow 3\times 2-4\times 3-8\Rightarrow L_{11}=6-12-8\Rightarrow c_1=-14$  

L₂₂  at $\left(-4,5\right)$  is given by

$L_{22}=3\times (-4)-4\times 5-8\Rightarrow L_2=-40$

Since $c_{1}and{c}_2$  are of same sign.

Therefore the two points are on the same side of the given line.