#### Answer

$d=\dfrac{a}{3}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
c=\dfrac{2cd}{a-d},
$ for $
d
,$ use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the properties of equality to isolate the variable, the equation above is equivalent to
\begin{array}{l}\require{cancel}
c=\dfrac{2cd}{a-d}
\\\\
(a-d)\cdot c=(a-d)\cdot \dfrac{2cd}{a-d}
\\\\
(a-d)c=2cd
\\\\
ac-dc=2cd
\\\\
-dc-2cd=-ac
\\\\
d(-c-2c)=-ac
\\\\
d=\dfrac{-ac}{-c-2c}
\\\\
d=\dfrac{-ac}{-3c}
\\\\
d=\dfrac{\cancel-a\cancel c}{\cancel-3\cancel c}
\\\\
d=\dfrac{a}{3}
.\end{array}