When two variables vary directly, it means that their ratio is constant. This can be expressed as:
\[ \frac{y}{x} = k \]
where \( k \) is the constant of variation.
Given that \( y = 84 \) when \( x = 12 \), we can first find the constant \( k \):
\[ k = \frac{y}{x} = \frac{84}{12} = 7 \]
Now that we have \( k \), we can use it to find \( y \) when \( x = 8 \):
\[ y = k \cdot x = 7 \cdot 8 = 56 \]
Therefore, when \( x = 8 \), \( y \) is:
\[ \boxed{56} \]