The point (-3, 2) lies on the line `ax + 3y + 6 = 0`, calculate the value of a. 

Answer

To find the value of \( a \) such that the point (-3, 2) lies on the line given by the equation \( ax + 3y + 6 = 0 \), we will substitute the coordinates of the point into the equation and solve for \( a \).

### Step-by-Step Solution:

1. **Write down the equation of the line:**
\[ ax + 3y + 6 = 0 \]

2. **Substitute the coordinates of the point (-3, 2) into the equation:**
- Here, \( x = -3 \) and \( y = 2 \).
\[ a(-3) + 3(2) + 6 = 0 \]

3. **Simplify the equation:**
- Calculate \( 3(2) \):
\[ a(-3) + 6 + 6 = 0 \]
- Combine like terms:
\[ -3a + 12 = 0 \]

4. **Isolate \( a \):**
- Move 12 to the other side:
\[ -3a = -12 \]

5. **Divide both sides by -3:**
\[ a = \frac{-12}{-3} = 4 \]

### Final Answer:
The value of \( a \) is \( 4 \).

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