The equation given is:

$4 = \frac{4}{3}(x + 6)$

The task is to isolate $x + 6$ by performing the same operation on both sides.

Step-by-step solution:

1. Multiply both sides by the reciprocal of $\frac{4}{3}$: To eliminate the fraction $\frac{4}{3}$ on the right-hand side, multiply both sides by the reciprocal, which is $\frac{3}{4}$.

   $\frac{3}{4} \times 4 = \frac{3}{4} \times \frac{4}{3}(x + 6)$

2. Simplify the left and right sides:

   $3 = x + 6$

Now, the expression for $x + 6$ is isolated.

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. How would you solve $3 = x + 6$ for $x$?
2. How can you check the solution for the equation $4 = \frac{4}{3}(x + 6)$?
3. What happens if the coefficient of $x + 6$ was $\frac{5}{3}$ instead of $\frac{4}{3}$?
4. Can you explain how to isolate $x$ in the equation $\frac{5}{2}(x + 4) = 10$?
5. How do you solve for $x$ if $\frac{7}{3}(x - 2) = 5$?

Tip:

Always remember to multiply by the reciprocal to eliminate fractions in an equation when solving for a variable.