Step 1: Set the common ratio:
Let $\frac{2x-1}{4} = \frac{1-y}{3} = \frac{-z}{6} = \mu$.
Now write $x$, $y$, $z$ in terms of $\mu$.
Step 2: Express the coordinates:
From the first part, $2x - 1 = 4\mu$, so $x = \frac{1}{2} + 2\mu$.
From the second, $1 - y = 3\mu$, so $y = 1 - 3\mu$.
From the third, $-z = 6\mu$, so $z = -6\mu$.
Step 3: Read the direction ratios:
The numbers multiplying $\mu$ are the direction ratios of the line.
They are $2, -3, -6$.
Step 4: Normalise:
The length is $\sqrt{4 + 9 + 36} = 7$.
So the direction cosines are $\frac{2}{7}, \frac{-3}{7}, \frac{-6}{7}$.
(The negative of all three, $-\frac{2}{7}, \frac{3}{7}, \frac{6}{7}$, is also valid for the opposite direction, but it is not an option.)
Step 5: Eliminate:
Option (A) is not normalised. Option (C) changes the sign of one value only, so it is not a direction of this line. Option (D) divides by $\sqrt{61}$, which comes from the wrong ratios $4, -3, -6$.
Final Answer:
Option (B) is correct. \[ \boxed{\left(\frac{2}{7}, \frac{-3}{7}, \frac{-6}{7}\right)} \]