Given that

$$ f(x)=x^2-4,\ and\ g(x)=x+3 $$

$$ f(g(x))=? $$

So,

$$ f(g(x))=f(x+3)=(x+3)^2-4=0 $$

$$ (x+3)^2=4 $$

$$ x+3=\pm 2 $$

$$ \therefore x=-1,\ x=-5 $$