20. As shown in the figure, the line $y=-x+3 \sqrt{2}$ intersects the $y$-axis and the $x$-axis at points $A$ and $B$, respectively. The line $AP$ intersects the $x$-axis at $P$. An isosceles right triangle $APC$ is constructed with $AP$ as one of its sides. The line $CB$ intersects the $y$-axis at point $D$. Then the length of $BD$ is $\qquad$.
$6$