If $\left|z-2-3i\right|+\left|z+2-6i\right|=4$ , where $i=\sqrt{-1}$ , then locus of $P\left(z\right)$  is:

$\left|z-z_1\right|+\left|z-z_2\right|=2a$ 

when  $|z_1-z_2|<2a$ , then it is an ellipse

         $z_1=2+3i$  and   $z_2=-2+6i$

     $z_1-z_2=\left(2+3i\right)-=4-3i$

$\left|z_1-z_2\right|=\left|4-3i\right|$

           $=\sqrt{4^2+{\left(-3\right)}^2}=5$

But $5<4$  is false, because in any triangle sum of two sides is not smaller than third side.

$\therefore P\left(z\right)$  is not represent locus of any point.