Multiply both sides of the equation by the lowest common denominator.

$\left(\frac{3}{5}=\frac{2x}{3}-8\right)\cdot15$

$3\cdot3=2x\cdot5-8\cdot15$

$9=10x-120$

$129 = 10x$

$12.9 = x$

Instead of removing fractions altogether, you may find it simplest to convert the second fraction so that it has the same denominator as the others. The denominator can be changed by multiplying the numerator and denominator by the same number.

Multiply by $6$ and then distribute.

$x=\frac{23}{9} \approx 2.56$