Answer
$6t^{11}-9t^9+\dfrac{9}{7}t^5$
Work Step by Step
Using $a(b+c)=ab+ac$ or the Distributive Property, the given expression, $
\dfrac{3}{4}t^5\left( 8t^6-12t^4+\dfrac{12}{7} \right)
$, is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{3}{4}t^5( 8t^6)+\dfrac{3}{4}t^5(-12t^4)+\dfrac{3}{4}t^5\left(\dfrac{12}{7} \right)
\\\\=
6t^{11}-9t^9+\dfrac{36}{28}t^5
\\\\=
6t^{11}-9t^9+\dfrac{9}{7}t^5
.\end{array}