The problem asks us to solve the proportion $\frac{3}{4} = \frac{2}{v-2}$.

1. Problem Description

The problem asks us to solve the proportion $\frac{3}{4} = \frac{2}{v-2}$.

2. Solution Steps

To solve the proportion $\frac{3}{4} = \frac{2}{v-2}$, we can cross-multiply. This means we multiply the numerator of the first fraction by the denominator of the second fraction, and set it equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$3(v-2) = 4(2)$

$3v - 6 = 8$

Now, we want to isolate $v$. Add 6 to both sides of the equation:

$3v - 6 + 6 = 8 + 6$

$3v = 14$

Divide both sides by 3 to solve for $v$:

$\frac{3v}{3} = \frac{14}{3}$

$v = \frac{14}{3}$

3. Final Answer

$v = \frac{14}{3}$