From the point $A\left(0,3\right)$ on the circle $x^2+4x+{\left(y-3\right)}^2=0,$ a chord $AB$ is drawn and extended from point $B$ to a point $M$ such that $AM=2AB.$ The perimeter of the locus of $M$ is $p\pi$ units. Then, the value of $p$ is

The equation of the given circle is
$x^2+y^2+4x-6y+9=0\dots \dots .\left(\mathrm{i}\right)$
Also, given that, $AM=2AB$
or $AB=BM$
Let, the coordinates of $M$ be $\left(h,k\right).$
Then, $B$ is the midpoint of $AM.$ Therefore,
$B\equiv \left(\frac{0+h}{2},\frac{3+k}{2}\right)\equiv \left(\frac{h}{2},\frac{k+3}{2}\right)$
As $B$ lies on the circle, we have, from $\left(\mathrm{i}\right)$,
$h^2+k^2+8h-6k+9=0$
$\Rightarrow$ locus is a circle with radius $4$
$\Rightarrow$ the perimeter of the locus is $8\pi$ units

$\Rightarrow p=8$