We are given that $x = \frac{1}{3}$ and $y = -\frac{1}{2}$. We need to find the value of the expression $(6x - 5)(4y - 1)$.

1. Problem Description

We are given that $x = \frac{1}{3}$ and $y = -\frac{1}{2}$.

We need to find the value of the expression $(6x - 5)(4y - 1)$.

2. Solution Steps

First, substitute the given values of $x$ and $y$ into the expression.

$$(6x - 5)(4y - 1) = \left(6\left(\frac{1}{3}\right) - 5\right)\left(4\left(-\frac{1}{2}\right) - 1\right)$$

Simplify the expression inside the first parenthesis:

$$6\left(\frac{1}{3}\right) - 5 = \frac{6}{3} - 5 = 2 - 5 = -3$$

Simplify the expression inside the second parenthesis:

$$4\left(-\frac{1}{2}\right) - 1 = -\frac{4}{2} - 1 = -2 - 1 = -3$$

Now multiply the two simplified expressions:

$$(6x - 5)(4y - 1) = (-3)(-3) = 9$$

3. Final Answer

The value of the expression $(6x - 5)(4y - 1)$ when $x = \frac{1}{3}$ and $y = -\frac{1}{2}$ is $9$.