Let's solve the equation step by step:

Given:
\[
\frac{2}{3}(3 - 6) - 3g = 3(5g - 4) - 2
\]

### Step 1: Simplify the expressions on both sides.
1. First, simplify \(\frac{2}{3}(3 - 6)\):
   \[
   \frac{2}{3}(-3) = -2
   \]
   So the equation becomes:
   \[
   -2 - 3g = 3(5g - 4) - 2
   \]

2. Distribute the \(3\) on the right-hand side:
   \[
   3(5g - 4) = 15g - 12
   \]
   Now the equation is:
   \[
   -2 - 3g = 15g - 12 - 2
   \]

3. Simplify the right-hand side further:
   \[
   -2 - 3g = 15g - 14
   \]

### Step 2: Collect like terms.
Move all the terms involving \(g\) to one side of the equation and the constants to the other side:
\[
-3g - 15g = -14 + 2
\]
Simplify:
\[
-18g = -12
\]

### Step 3: Solve for \(g\).
Divide both sides by \(-18\):
\[
g = \frac{-12}{-18} = \frac{2}{3}
\]

### Final Answer:
\[
g = \frac{2}{3}
\]

Would you like more details or have any questions about the solution? Here are some related questions you might find helpful:

1. How do you distribute fractions in algebraic expressions?
2. What are the steps to move terms across the equal sign?
3. How do you simplify expressions with negative signs?
4. What are some common mistakes to avoid when solving linear equations?
5. Can you explain how to check if the solution is correct?

**Tip:** Always double-check your distribution and sign changes to avoid errors in solving equations!

Learn how to solve the equation 2/3(3-6)-3g=3(5g-4)-2 with a detailed step-by-step solution. This problem covers algebraic concepts such as equations and the distributive property. Suitable for students in Grades 7-9.

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