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The given equation is:

\[
\frac{2}{3}x + \frac{4}{3} = -\frac{4}{3}
\]

### Step-by-step solution:

1. First, subtract \(\frac{4}{3}\) from both sides to isolate the term with \(x\):

\[
\frac{2}{3}x = -\frac{4}{3} - \frac{4}{3}
\]

2. Simplify the right-hand side:

\[
\frac{2}{3}x = -\frac{8}{3}
\]

3. Now, solve for \(x\) by multiplying both sides of the equation by the reciprocal of \(\frac{2}{3}\), which is \(\frac{3}{2}\):

\[
x = \left(-\frac{8}{3}\right) \times \frac{3}{2} = -\frac{8}{2} = -4
\]

Thus, the solution is:

\[
x = -4
\]

Would you like more details or have any other questions?

### Related questions:
1. How would the solution change if the constant term were different?
2. What are some common strategies for solving fractional linear equations?
3. Can you demonstrate solving a similar equation with different coefficients?
4. What happens if the fractions were more complex, e.g., different denominators?
5. How can I check the solution of a fractional equation like this?

### Tip:
Always simplify both sides of the equation first to make solving easier, especially when dealing with fractions.

Step-by-step guide to solving the linear fraction equation (2/3)x + 4/3 = -4/3. This problem covers algebraic concepts, including isolating variables and dealing with fractions. Suitable for students in Grades 6-8.

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