To solve for the other solution given that one solution is \( x = -\frac{4}{3} \) for the equation \( (6x + 4)^2 = 0 \), we first need to analyze the equation.
First, set the expression inside the square equal to zero:
\[ (6x + 4)^2 = 0 \]
Taking the square root of both sides gives:
\[ 6x + 4 = 0 \]
Now, we can solve for \( x \):
\[ 6x = -4 \]
\[ x = -\frac{4}{6} = -\frac{2}{3} \]
So, the other solution is:
\[ x = -\frac{2}{3} \]
Thus, the solutions are:
- First solution: \( x = -\frac{4}{3} \)
- Other solution: \( x = -\frac{2}{3} \)