<image>$$P_{1}(x_{1},y_{1})$$ and $$P_{2}(x_{2},y_{2})$$ are any two points in the Cartesian coordinate plane. We refer to $$|x_{1}-x_{2}|+|y_{1}-y_{2}|$$ as the "right-angle distance" between points $$P_{1}$$ and $$P_{2}$$, denoted as $$d(P_{1},P_{2}).$$
$$(1)$$ Let $$P_{0}(2,-4)$$ and $$O$$ be the origin. Then $$d(O,P_{0})=$$ ______ ;
$$(2)$$ Given $$Q(2,1)$$, a moving point $$P(x,y)$$ satisfies $$d(Q,P)=3$$, and both $$x$$ and $$y$$ are integers.
$$①$$ How many points $$P$$ satisfy the condition?
$$②$$ If point $$P$$ lies on the line $$y=3x$$, please provide the coordinates of all such points $$P$$.