Answer
$$ - 960\,740\,352{c^7}{d^7}$$
Work Step by Step
$$\eqalign{
& {\text{eighth term of }}{\left( {2c - 3d} \right)^{14}} \cr
& {\text{In the eighth term, }} - 3d{\text{ has an exponent of 8}} - 1,{\text{ or 7, while }}2c \cr
& {\text{has an exponent of 14}} - 7,{\text{ or 7}}{\text{.}} \cr
& \cr
& {\text{Using the }}k{\text{th Term of The Binomial Expansion}} \cr
& {\text{eighth term}} = \left( {14{\bf{C}}7} \right){\left( {2c} \right)^7}{\left( { - 3d} \right)^7} \cr
& {\text{eighth term}} = \frac{{14!}}{{7!7!}}\left( {128{c^7}} \right)\left( {2187{d^7}} \right) \cr
& {\text{eighth term}} = 3432\left( {128{c^7}} \right)\left( { - 2187{d^7}} \right) \cr
& {\text{eighth term}} = - 960\,740\,352{c^7}{d^7} \cr} $$
