यदि 3 tanθ = 2 है, तो (2sinθ - cosθ) / (2cosθ - sinθ) का मान ज्ञात करें।

We are given $3 \tan \theta = 2$.
Dividing both sides by 3, we get:

$$\tan \theta = \frac{2}{3}$$

The expression is $\frac{2\sin\theta - \cos\theta}{2\cos\theta - \sin\theta}$.
Divide each term in the numerator and denominator by $\cos\theta$:

$$\frac{\frac{2\sin\theta}{\cos\theta} - \frac{\cos\theta}{\cos\theta}}{\frac{2\cos\theta}{\cos\theta} - \frac{\sin\theta}{\cos\theta}}$$

Since $\frac{\sin\theta}{\cos\theta} = \tan\theta$ and $\frac{\cos\theta}{\cos\theta} = 1$, the expression becomes:

$$\frac{2\tan\theta - 1}{2 - \tan\theta}$$

Substitute $\tan\theta = \frac{2}{3}$:

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

Calculate the numerator:

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

Calculate the denominator:

$$2 - \frac{2}{3} = \frac{6}{3} - \frac{2}{3} = \frac{6-2}{3} = \frac{4}{3}$$

Now, divide the numerator by the denominator:

$$\frac{\frac{1}{3}}{\frac{4}{3}} = \frac{1}{3} \times \frac{3}{4} = \frac{1}{4}$$

The value of the expression is $\frac{1}{4}$. This corresponds to option (c).