Answer
$r=-\frac{4}{9}$.
Work Step by Step
The given expression is
$\Rightarrow \frac{3}{8}r+\frac{5}{6}=\frac{2}{3}$
Multiply by the LCD =24.
$\Rightarrow 24\left ( \frac{3}{8}r+\frac{5}{6} \right )=24\left (\frac{2}{3}\right )$
Use distributive property.
$\Rightarrow 24\left ( \frac{3}{8}r\right )+24\left ( \frac{5}{6} \right )=24\left (\frac{2}{3}\right )$
Simplify.
$\Rightarrow 9r+20=16$
Subtract $20$ from both sides.
$\Rightarrow 9r+20-20=16-20$
Simplify.
$\Rightarrow 9r=-4$
Divide both sides by $9$.
$\Rightarrow \frac{9r}{9}=\frac{-4}{9}$
Simplify.
$\Rightarrow r=-\frac{4}{9}$.