The lines represented by `4x + 3y = 9` and `px - 6y + 3 = 0` are parallel. Find the value of p. 

Answer

To find the value of \( p \) such that the lines represented by the equations \( 4x + 3y = 9 \) and \( px - 6y + 3 = 0 \) are parallel, we will follow these steps:

### Step 1: Find the slope of the first line
The first line is given by the equation:
\[ 4x + 3y = 9 \]
We can rearrange this equation into the slope-intercept form \( y = mx + c \).

1. Subtract \( 4x \) from both sides:
\[ 3y = 9 - 4x \]
2. Divide every term by \( 3 \):
\[ y = -\frac{4}{3}x + 3 \]

From this, we can see that the slope \( m_1 \) of the first line is:
\[ m_1 = -\frac{4}{3} \]

### Step 2: Find the slope of the second line
The second line is given by the equation:
\[ px - 6y + 3 = 0 \]
We will also rearrange this into the slope-intercept form.

1. Move \( px \) and \( 3 \) to the right side:
\[ -6y = -px - 3 \]
2. Divide every term by \( -6 \):
\[ y = \frac{p}{6}x + \frac{3}{6} \]
Simplifying \( \frac{3}{6} \) gives:
\[ y = \frac{p}{6}x + \frac{1}{2} \]

From this, we can see that the slope \( m_2 \) of the second line is:
\[ m_2 = \frac{p}{6} \]

### Step 3: Set the slopes equal to each other
Since the lines are parallel, their slopes must be equal:
\[ m_1 = m_2 \]
Substituting the values we found:
\[ -\frac{4}{3} = \frac{p}{6} \]

### Step 4: Solve for \( p \)
To solve for \( p \), we can cross-multiply:
\[ -4 \cdot 6 = 3p \]
This simplifies to:
\[ -24 = 3p \]
Now, divide both sides by \( 3 \):
\[ p = -8 \]

### Final Answer
The value of \( p \) is:
\[ \boxed{-8} \]