dividing a fraction by a fraction is the same as multiplying a fraction by the reciprocal of another fraction...like this:
\[\huge{{a\over b}\over{c\over d}}~~~~~\implies~~~~~{{a\over b}\times{d\over c}}\]
so in your case its:\[\huge{{12x\over x^2+6x+9}\over{4x^2\over x^2-9}}~~~~~\implies~~~~~{{12x\over x^2+6x+9}\times{x^2-9\over4x^2}}\] so now just cross multiply
\[\large{{12x\over x^2+6x+9}\times{x^2-9\over4x^2}}~~~~~\implies~~~~{{12x\times(x^2-9)}\over{x^2+6x+9\times (4x^2)}}\]sorry i wrote that wrong...this gives you:\[\large{12x^3-108x\over 4x^4+24x^3+36x^2}\]simpllify that