Chapter 2 - Linear and Quadratic Functions - Section 2.3 Quadratic Functions and Their Zeros - 2.3 Assess Your Understanding - Page 146: 21

the zeros are $x=-6$ or $x=-2$ and the $x$-intercepts are $(-6,0)$ and $(-2,0)$.

By factorization, we have $$ g(x)=x(x+8)+12=x^2+8x+12=(x+6)(x+2) .$$ That is, we have $x+6=0 $ or $x+2=0$. So the zeros are $x=-6$ or $x=-2$ and the $x$-intercepts are $(-6,0)$ and $(-2,0)$.