Since \( x \) varies inversely with \( y \), we can express this relationship as:
\[ x \cdot y = k \]
where \( k \) is a constant. From the information given, when \( y = 3 \) and \( x = 8 \), we can find \( k \):
\[ 8 \cdot 3 = k \implies k = 24 \]
Now we can set up the equation with the constant:
\[ x \cdot y = 24 \]
We want to find \( x \) when \( y = 4 \):
\[ x \cdot 4 = 24 \]
To solve for \( x \):
\[ x = \frac{24}{4} = 6 \]
Therefore, the correct answer is:
\( x = 6 \).