The problem asks to evaluate the expression: $\frac{1}{4} \times \frac{3}{2} \times (-\frac{2}{3})$.

1. Problem Description

The problem asks to evaluate the expression: $\frac{1}{4} \times \frac{3}{2} \times (-\frac{2}{3})$.

2. Solution Steps

To solve this, we multiply the fractions together.

Recall that when multiplying fractions, we multiply the numerators together and the denominators together.

Also remember that a positive times a negative is a negative.

$\frac{1}{4} \times \frac{3}{2} \times (-\frac{2}{3}) = \frac{1 \times 3 \times (-2)}{4 \times 2 \times 3} = \frac{-6}{24}$

Now we simplify the fraction. We can divide both the numerator and the denominator by

6.

$\frac{-6}{24} = -\frac{6}{24} = -\frac{6 \div 6}{24 \div 6} = -\frac{1}{4}$

3. Final Answer

The final answer is $-\frac{1}{4}$.