Answer
$\dfrac{3}{16}x^4+7x^2-96$
Work Step by Step
Using $(a+b)(c+d)=ab+ad+bc+bd$ or the FOIL Method, the product of the given expression, $
\left( \dfrac{1}{4}x^2+12 \right)\left( \dfrac{3}{4}x^2-8 \right)
,$ is
\begin{array}{l}\require{cancel}
\dfrac{1}{4}x^2\left( \dfrac{3}{4}x^2 \right)+\dfrac{1}{4}x^2(-8)+12\left(\dfrac{3}{4}x^2\right)+12(-8)
\\\\=
\dfrac{3}{16}x^4-2x^2+9x^2-96
\\\\=
\dfrac{3}{16}x^4+7x^2-96
.\end{array}
