To solve the equation 6/5 : 2x - 4/3 = -5/2, we can start by simplifying the left side of the equation.

First, we can simplify 6/5 by multiplying both the numerator and denominator by 3 to get 18/15.

So, the equation becomes:

18/15 : 2x - 4/3 = -5/2

Next, we can simplify the right side of the equation by multiplying both the numerator and denominator of -5/2 by 15 to get -75/30.

Now, the equation becomes:

18/15 : 2x - 4/3 = -75/30

To simplify the equation further, we can multiply both sides by 15 to get rid of the denominators:

(18/15) * 15 : (2x - 4/3) * 15 = (-75/30) * 15

This simplifies to:

18 : 15(2x - 4/3) = -75 * 15/30

Now, we can simplify the equation even more:

18 : 30x - 20/3 = -75/2

To get rid of the fraction, we can multiply both sides by 3:

3 * (18 : 30x - 20/3) = 3 * (-75/2)

This simplifies to:

54 : 90x - 20 = -225/2

Next, we can multiply both sides by 2 to get rid of the fraction:

2 * (54 : 90x - 20) = 2 * (-225/2)

This simplifies to:

108 : 180x - 40 = -225

Finally, we can add 40 to both sides of the equation:

108 : 180x - 40 + 40 = -225 + 40

This simplifies to:

108 : 180x = -185

To solve for x, we can cross-multiply:

108 * x = 180 * -185

108x = -33300

Divide both sides by 108 to solve for x:

x = -33300/108

Simplifying the fraction gives:

x = -275

Therefore, the solution to the equation 6/5 : 2x - 4/3 = -5/2 is x = -275.