`{:(3x - 2y = 6),((x)/(3) - (y)/(6) = (1)/(2)):}`

Answer

To solve the system of equations given by:

1. \(3x - 2y = 6\) (Equation 1)
2. \(\frac{x}{3} - \frac{y}{6} = \frac{1}{2}\) (Equation 2)

we will follow these steps:

### Step 1: Simplify Equation 2
First, we will eliminate the fractions in Equation 2 by multiplying the entire equation by 6 (the least common multiple of the denominators).

\[ 6 \left(\frac{x}{3}\right) - 6 \left(\frac{y}{6}\right) = 6 \left(\frac{1}{2}\right) \]

This simplifies to:

\[ 2x - y = 3 \quad \text{(Equation 3)} \]

### Step 2: Express y in terms of x
From Equation 3, we can express \(y\) in terms of \(x\):

\[ y = 2x - 3 \quad \text{(Equation 4)} \]

### Step 3: Substitute Equation 4 into Equation 1
Now, we will substitute Equation 4 into Equation 1 to find the value of \(x\):

\[ 3x - 2(2x - 3) = 6 \]

Expanding this gives:

\[ 3x - 4x + 6 = 6 \]

### Step 4: Solve for x
Now, we simplify the equation:

\[ -1x + 6 = 6 \]

Subtracting 6 from both sides:

\[ -1x = 0 \]

Thus, we find:

\[ x = 0 \]

### Step 5: Substitute x back into Equation 4
Now that we have \(x\), we will substitute it back into Equation 4 to find \(y\):

\[ y = 2(0) - 3 \]

This simplifies to:

\[ y = -3 \]

### Final Solution
The solution to the system of equations is:

\[ (x, y) = (0, -3) \]