$\frac{2}{3} x-10=-12$

Step 1 ：The given equation is \( \frac{2}{3} x - 10 = -12 \)

Step 2 ：First, add 10 to both sides of the equation to get rid of the -10 on the left side. This gives us \( \frac{2}{3} x = -12 + 10 \)

Step 3 ：Then, multiply both sides of the equation by \( \frac{3}{2} \) to solve for x. This gives us \( x = \frac{3}{2}(-12 + 10) \)

Step 4 ：Calculate the value of x to get \( x = -3.0 \)

Step 5 ：Final Answer: The solution to the equation \( \frac{2}{3} x - 10 = -12 \) is \( \boxed{-3} \)