#### Answer

$\color{blue}{-\dfrac{17}{15}}$

#### Work Step by Step

Multiply $3p+4$ to both sides of the equation to obtain:
$10(3p+4) = \dfrac{6}{3p+4} \cdot (3p+4)
\\10(3p)+10(4)=6
\\30p+40=6$
Subtract $40$ to both sides of the equation to obtain:
$30p=6-40
\\30w=-34$
Divide $30$ to both sides to obtain:
$p = -\frac{34}{30}
\\p=-\frac{17}{15}$
Cheking:
$10=\dfrac{6}{3p+4}?
\\10 = \dfrac{6}{3\cdot(-\frac{17}{15})+4}?
\\10=\dfrac{6}{-\frac{17}{5}+4}?
\\10=\dfrac{6}{-\frac{17}{5} + \frac{20}{5}}?
\\10=\dfrac{6}{\frac{3}{5}}?
\\10=6 \cdot \frac{5}{3}?
\\10=10$
Thus, the solution to the given equation is: $\color{blue}{-\dfrac{17}{15}}$.