The directrix of the parabola `x^(2) = 6y ` is y = `- (3)/(2) ` .

Answer

To find the directrix of the parabola given by the equation \( x^2 = 6y \), we can follow these steps:

### Step 1: Identify the standard form of the parabola
The standard form of a parabola that opens upwards is given by:
\[ x^2 = 4ay \]
where \( a \) is the distance from the vertex to the focus, and also from the vertex to the directrix.

### Step 2: Compare the given equation with the standard form
We have the equation:
\[ x^2 = 6y \]
Now, we can compare this with the standard form \( x^2 = 4ay \).

### Step 3: Determine the value of \( a \)
From the comparison, we can see that:
\[ 4a = 6 \]
To find \( a \), we divide both sides by 4:
\[ a = \frac{6}{4} = \frac{3}{2} \]

### Step 4: Find the equation of the directrix
The directrix of a parabola that opens upwards is given by the equation:
\[ y = -a \]
Substituting the value of \( a \):
\[ y = -\frac{3}{2} \]

### Conclusion
Thus, the directrix of the parabola \( x^2 = 6y \) is:
\[ y = -\frac{3}{2} \]

---