It is easier to work with the form of equation after completing the square.
g(x)=4x^2+24x+30=4(x^2+6x+9)-6=4(x+3)^2-6
If the parent function is f(x)=x^2, then the transformations are
g(x)=a*f(x-h)+k
where
a=vertical stretching factor
h=horizontal shift
k=vertical shift
where, by comparison, a=4, h=-3, k=-6
Thus the transformations are
horizontal shift of -3 (i.e. to the left)
vertical scale factor of 4 (stretch)
vertical shift of -6 (down)