we have the functions
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=x^2+8x+16 \end{gathered}[/tex]The vertex of function f(x) is the origin (0,0)
so
Find out the vertex of the function g(x)
Convert to vertex form
Complete the square
[tex]\begin{gathered} g(x)=(x^2+8x)+16 \\ g(x)=(x^2+8x+4^2)+16-4^2 \\ g(x)=(x+4)^2 \end{gathered}[/tex]The vertex of the function g(x) is (-4,0)
therefore
The rule of the translation is given by
(x,y) -------> (x-4,y)
