Let  $P_1$ be a parabola with vertex $\left(3,2\right)$ and focus $\left(4,4\right)$ and $P_2$  be its mirror image with respect to the line  $x+2y=6$, Then the directrix of $P_2$  is $x+2y=$ ______.

Vertex and focus of parabola $P_1$  are A(3, 2) and B(4,4) respectively. If C is the foot of perpendicular on the axis of the parabola. Then $C\equiv (2,0).$  Ab is the axis of the parabola. Its slope is 2. 
So, equation of directrix is  $x+2y=2$.
Its image in the line  $x+2y=6isx+2y=10$.