To solve the equation
\[ \frac{x}{3} - \frac{5}{6} = \frac{3(x - 3)}{12}, \]
let's start by simplifying the right side.
We know that:
\[ \frac{3(x - 3)}{12} = \frac{x - 3}{4} \]
This gives us the equation:
\[ \frac{x}{3} - \frac{5}{6} = \frac{x - 3}{4} \]
Next, let's eliminate the fractions by finding a common denominator. The denominators are 3, 6, and 4. The least common multiple of these numbers is 12.
We will multiply every term in the equation by 12:
\[ 12 \left(\frac{x}{3}\right) - 12 \left(\frac{5}{6}\right) = 12 \left(\frac{x - 3}{4}\right) \]
Simplifying each term:
- \( 12 \cdot \frac{x}{3} = 4x \)
- \( 12 \cdot \frac{5}{6} = 10 \)
- \( 12 \cdot \frac{x - 3}{4} = 3(x - 3) = 3x - 9 \)
Now we have:
\[ 4x - 10 = 3x - 9 \]
Next, let's isolate \( x \) by moving \( 3x \) to the left side:
\[ 4x - 3x - 10 = -9 \]
This simplifies to:
\[ x - 10 = -9 \]
Now add 10 to both sides:
\[ x = 1 \]
Thus, the solution is:
\[ \boxed{1} \]
So, the correct answer is B. x = 1.